$SPAD/src/input richerror000-078.input

Albert Rich and Timothy Daly

December 3, 2016

Abstract

Contents

2

— * —

)set break resume
)sys rm -f richerror000-078.output
)spool richerror000-078.output
)set message auto off
)clear all
--S 1 of 395
t0000:= erf(b*x)^2/x^7
--R
--R
--R                2
--R        erf(b x)
--R   (1)  ---------
--R             7
--R            x
--R                                                    Type: Expression(Integer)
--E 1
--S 2 of 395
r0000:= -1/15*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^4+2/9*b^4/_
        (exp(1)^(2*b^2*x^2))/%pi/x^2-2/45*b*(3-2*b^2*x^2+_
        4*b^4*x^4)*erf(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/_
        x^5-4/45*b^6*erf(b*x)^2-1/6*erf(b*x)^2/x^6+_
        28/45*b^6*Ei(-2*b^2*x^2)/%pi
--R
--R
--R   (2)
--R                                                                  2 2    2 2
--R                 6     6                 2      6 6       2 2    b x   2b x
--R           ((- 8b %pi x  - 15%pi)erf(b x)  + 56b x Ei(- 2b x ))%e    %e
--R         +
--R                              2 2
--R               4 4     2 2   b x
--R           (20b x  - 6b x )%e
--R      *
--R          +---+
--R         \|%pi
--R     +
--R                                                         2 2
--R             5     5     3     3                       2b x
--R       (- 16b %pi x  + 8b %pi x  - 12b %pi x)erf(b x)%e
--R  /
--R                2 2    2 2
--R            6  b x   2b x  +---+
--R     90%pi x %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 2

--S 3 of 395
a0000:= integrate(t0000,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 3
--S 4 of 395
--m0000:= a0000-r0000
--E 4
--S 5 of 395
--d0000:= D(m0000,x)
--E 5
--S 6 of 395
t0001:= erf(b*x)^2/x^5
--R
--R
--R                2
--R        erf(b x)
--R   (3)  ---------
--R             5
--R            x
--R                                                    Type: Expression(Integer)
--E 6
--S 7 of 395
r0001:= -1/3*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^2-_
        1/3*b*(1-2*b^2*x^2)*erf(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x^3+_
        1/3*b^4*erf(b*x)^2-1/4*erf(b*x)^2/x^4-4/3*b^4*Ei(-2*b^2*x^2)/%pi
--R
--R
--R   (4)
--R                                                               2 2    2 2
--R               4     4                2      4 4       2 2    b x   2b x
--R           ((4b %pi x  - 3%pi)erf(b x)  - 16b x Ei(- 2b x ))%e    %e
--R         +
--R                     2 2
--R               2 2  b x
--R           - 4b x %e
--R      *
--R          +---+
--R         \|%pi
--R     +

--R                                         2 2
--R          3     3                      2b x
--R       (8b %pi x  - 4b %pi x)erf(b x)%e
--R  /
--R                2 2    2 2
--R            4  b x   2b x  +---+
--R     12%pi x %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 7
--S 8 of 395
a0001:= integrate(t0001,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 8
--S 9 of 395
--m0001:= a0001-r0001
--E 9
--S 10 of 395
--d0001:= D(m0001,x)
--E 10
--S 11 of 395
t0002:= erf(b*x)^2/x^3
--R
--R
--R                2
--R        erf(b x)
--R   (5)  ---------
--R             3
--R            x
--R                                                    Type: Expression(Integer)
--E 11
--S 12 of 395
r0002:= -2*b*erf(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x-b^2*erf(b*x)^2-_
        1/2*erf(b*x)^2/x^2+2*b^2*Ei(-2*b^2*x^2)/%pi
--R
--R
--R   (6)
--R                                                           2 2
--R             2     2               2     2 2       2 2    b x  +---+
--R       ((- 2b %pi x  - %pi)erf(b x)  + 4b x Ei(- 2b x ))%e    \|%pi

--R     +
--R       - 4b %pi x erf(b x)
--R  /
--R               2 2
--R           2  b x  +---+
--R     2%pi x %e    \|%pi
--R                                                    Type: Expression(Integer)
--E 12
--S 13 of 395
a0002:= integrate(t0002,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 13
--S 14 of 395
--m0002:= a0002-r0002
--E 14
--S 15 of 395
--d0002:= D(m0002,x)
--E 15
--S 16 of 395
t0003:= x*erf(b*x)^2
--R
--R
--R                  2
--R   (7)  x erf(b x)
--R                                                    Type: Expression(Integer)
--E 16
--S 17 of 395
r0003:= 1/2/(exp(1)^(2*b^2*x^2))/b^2/%pi+x*erf(b*x)/(exp(1)^(b^2*x^2))/_
        b/%pi^(1/2)-1/4*erf(b*x)^2/b^2+1/2*x^2*erf(b*x)^2
--R
--R
--R   (8)
--R                                     2 2    2 2       2 2
--R           2     2               2  b x   2b x       b x   +---+
--R       ((2b %pi x  - %pi)erf(b x) %e    %e      + 2%e    )\|%pi
--R     +
--R                            2 2
--R                          2b x
--R       4b %pi x erf(b x)%e

--R  /
--R               2 2    2 2
--R       2      b x   2b x  +---+
--R     4b %pi %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 17
--S 18 of 395
a0003:= integrate(t0003,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 18
--S 19 of 395
--m0003:= a0003-r0003
--E 19
--S 20 of 395
--d0003:= D(m0003,x)
--E 20
--S 21 of 395
t0004:= x^3*erf(b*x)^2
--R
--R
--R         3        2
--R   (9)  x erf(b x)
--R                                                    Type: Expression(Integer)
--E 21
--S 22 of 395
r0004:= 1/2/(exp(1)^(2*b^2*x^2))/b^4/%pi+1/4*x^2/(exp(1)^(2*b^2*x^2))/b^2/%pi+_
        1/4*x*(3+2*b^2*x^2)*erf(b*x)/(exp(1)^(b^2*x^2))/b^3/%pi^(1/2)-_
        3/16*erf(b*x)^2/b^4+1/4*x^4*erf(b*x)^2
--R
--R
--R   (10)
--R                                      2 2    2 2                 2 2
--R           4     4                2  b x   2b x       2 2       b x   +---+
--R       ((4b %pi x  - 3%pi)erf(b x) %e    %e      + (4b x  + 8)%e    )\|%pi
--R     +
--R                                          2 2
--R          3     3                       2b x
--R       (8b %pi x  + 12b %pi x)erf(b x)%e
--R  /

--R                2 2    2 2
--R        4      b x   2b x  +---+
--R     16b %pi %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 22
--S 23 of 395
a0004:= integrate(t0004,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 23
--S 24 of 395
--m0004:= a0004-r0004
--E 24
--S 25 of 395
--d0004:= D(m0004,x)
--E 25
--S 26 of 395
t0005:= x^5*erf(b*x)^2
--R
--R
--R          5        2
--R   (11)  x erf(b x)
--R                                                    Type: Expression(Integer)
--E 26
--S 27 of 395
r0005:= 11/12/(exp(1)^(2*b^2*x^2))/b^6/%pi+7/12*x^2/(exp(1)^(2*b^2*x^2))/_
        b^4/%pi+1/6*x^4/(exp(1)^(2*b^2*x^2))/b^2/%pi+1/12*x*(15+10*b^2*x^2+_
        4*b^4*x^4)*erf(b*x)/(exp(1)^(b^2*x^2))/b^5/%pi^(1/2)-_
        5/16*erf(b*x)^2/b^6+1/6*x^6*erf(b*x)^2
--R
--R
--R   (12)
--R                                            2 2    2 2
--R                6     6                 2  b x   2b x
--R             (8b %pi x  - 15%pi)erf(b x) %e    %e
--R           +
--R                                     2 2
--R                4 4      2 2        b x
--R             (8b x  + 28b x  + 44)%e
--R      *

--R          +---+
--R         \|%pi
--R     +
--R                                                        2 2
--R           5     5      3     3                       2b x
--R       (16b %pi x  + 40b %pi x  + 60b %pi x)erf(b x)%e
--R  /
--R                2 2    2 2
--R        6      b x   2b x  +---+
--R     48b %pi %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 27
--S 28 of 395
a0005:= integrate(t0005,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 28
--S 29 of 395
--m0005:= a0005-r0005
--E 29
--S 30 of 395
--d0005:= D(m0005,x)
--E 30
--S 31 of 395
t0006:= x*erf(a+b*x)^2
--R
--R
--R                       2
--R   (13)  x erf(b x + a)
--R                                                    Type: Expression(Integer)
--E 31
--S 32 of 395
r0006:= 1/4/b^2*(2/(exp(1)^(2*(a+b*x)^2))/%pi-_
        4*(a-b*x)*erf(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)-erf(a+b*x)^2-_
        4*a*(a+b*x)*erf(a+b*x)^2+2*(a+b*x)^2*erf(a+b*x)^2+_
        4*a*2^(1/2)/%pi^(1/2)*erf(2^(1/2)*(a+b*x)))
--R
--R
--R   (14)
--R                                                         2 2             2

--R                2     2        2                     2  b x  + 2a b x + a
--R             (2b %pi x  + (- 2a  - 1)%pi)erf(b x + a) %e
--R          *
--R                 2 2              2
--R               2b x  + 4a b x + 2a
--R             %e
--R         +
--R               2 2             2
--R              b x  + 2a b x + a
--R           2%e
--R      *
--R          +---+
--R         \|%pi
--R     +
--R                                          2 2             2
--R                  +-+              +-+   b x  + 2a b x + a
--R           4a %pi\|2 erf((b x + a)\|2 )%e
--R         +
--R           (4b %pi x - 4a %pi)erf(b x + a)
--R      *
--R             2 2              2
--R           2b x  + 4a b x + 2a
--R         %e
--R  /
--R               2 2             2    2 2              2
--R       2      b x  + 2a b x + a   2b x  + 4a b x + 2a  +---+
--R     4b %pi %e                  %e                    \|%pi
--R                                                    Type: Expression(Integer)
--E 32
--S 33 of 395
a0006:= integrate(t0006,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 33
--S 34 of 395
--m0006:= a0006-r0006
--E 34
--S 35 of 395
--d0006:= D(m0006,x)
--E 35
--S 36 of 395

t0007:= x^2*erf(a+b*x)^2
--R
--R
--R          2            2
--R   (15)  x erf(b x + a)
--R                                                    Type: Expression(Integer)
--E 36
--S 37 of 395
r0007:= -1/6/b^3*(4*a/(exp(1)^(2*(a+b*x)^2))/%pi-_
        2*b*x/(exp(1)^(2*(a+b*x)^2))/%pi-_
        4*(1+a^2-a*b*x+b^2*x^2)*erf(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)-_
        3*a*erf(a+b*x)^2-6*a^2*(a+b*x)*erf(a+b*x)^2+_
        6*a*(a+b*x)^2*erf(a+b*x)^2-2*(a+b*x)^3*erf(a+b*x)^2+_
        1/2*(5+12*a^2)*erf(2^(1/2)*(a+b*x))*2^(1/2)/%pi^(1/2))
--R
--R
--R   (16)
--R                                                        2 2             2
--R                3     3      3                      2  b x  + 2a b x + a
--R             (4b %pi x  + (4a  + 6a)%pi)erf(b x + a) %e
--R          *
--R                 2 2              2
--R               2b x  + 4a b x + 2a
--R             %e
--R         +
--R                         2 2             2
--R                        b x  + 2a b x + a
--R           (4b x - 8a)%e
--R      *
--R          +---+
--R         \|%pi
--R     +
--R                                                   2 2             2
--R                 2         +-+              +-+   b x  + 2a b x + a
--R           (- 12a  - 5)%pi\|2 erf((b x + a)\|2 )%e
--R         +
--R              2     2                   2
--R           (8b %pi x  - 8a b %pi x + (8a  + 8)%pi)erf(b x + a)
--R      *
--R             2 2              2
--R           2b x  + 4a b x + 2a
--R         %e
--R  /
--R                2 2             2    2 2              2
--R        3      b x  + 2a b x + a   2b x  + 4a b x + 2a  +---+
--R     12b %pi %e                  %e                    \|%pi
--R                                                    Type: Expression(Integer)
--E 37

--S 38 of 395
a0007:= integrate(t0007,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 38
--S 39 of 395
--m0007:= a0007-r0007
--E 39
--S 40 of 395
--d0007:= D(m0007,x)
--E 40
--S 41 of 395
t0008:= exp(1)^(-b^2*x^2)*erf(b*x)/x^8
--R
--R
--R                      2 2
--R                   - b x
--R         erf(b x)%e
--R   (17)  ----------------
--R                 8
--R                x
--R                                                    Type: Expression(Integer)
--E 41
--S 42 of 395
r0008:= -1/21*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^6+_
        8/105*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4-_
        4/21*b^5/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-1/105*(15-6*b^2*x^2+_
        4*b^4*x^4-8*b^6*x^6)*erf(b*x)/(exp(1)^(b^2*x^2))/x^7+_
        4/105*b^7*%pi^(1/2)*erf(b*x)^2-16/35*b^7*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R
--R   (18)
--R                                               2 2
--R          6 6     4 4     2 2                2b x  +---+
--R       (8b x  - 4b x  + 6b x  - 15)erf(b x)%e     \|%pi
--R     +
--R                                                  2 2    2 2
--R          7     7        2      7 7       2 2    b x   2b x
--R       (4b %pi x erf(b x)  - 48b x Ei(- 2b x ))%e    %e
--R     +
--R                                   2 2

--R             5 5     3 3          b x
--R       (- 20b x  + 8b x  - 5b x)%e
--R  /
--R             2 2    2 2
--R         7  b x   2b x  +---+
--R     105x %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 42
--S 43 of 395
a0008:= integrate(t0008,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 43
--S 44 of 395
--m0008:= a0008-r0008
--E 44
--S 45 of 395
--d0008:= D(m0008,x)
--E 45
--S 46 of 395
t0009:= exp(1)^(-b^2*x^2)*erf(b*x)/x^6
--R
--R
--R                      2 2
--R                   - b x
--R         erf(b x)%e
--R   (19)  ----------------
--R                 6
--R                x
--R                                                    Type: Expression(Integer)
--E 46
--S 47 of 395
r0009:= -1/10*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4+_
        1/3*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_
        1/15*(3-2*b^2*x^2+4*b^4*x^4)*erf(b*x)/(exp(1)^(b^2*x^2))/x^5-_
        2/15*b^5*%pi^(1/2)*erf(b*x)^2+14/15*b^5*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R
--R   (20)
--R                                        2 2

--R            4 4     2 2               2b x  +---+
--R       (- 8b x  + 4b x  - 6)erf(b x)%e     \|%pi
--R     +
--R                                                    2 2    2 2
--R            5     5        2      5 5       2 2    b x   2b x
--R       (- 4b %pi x erf(b x)  + 28b x Ei(- 2b x ))%e    %e
--R     +
--R                         2 2
--R           3 3          b x
--R       (10b x  - 3b x)%e
--R  /
--R            2 2    2 2
--R        5  b x   2b x  +---+
--R     30x %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 47
--S 48 of 395
a0009:= integrate(t0009,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 48
--S 49 of 395
--m0009:= a0009-r0009
--E 49
--S 50 of 395
--d0009:= D(m0009,x)
--E 50
--S 51 of 395
t0010:= exp(1)^(-b^2*x^2)*erf(b*x)/x^4
--R
--R
--R                      2 2
--R                   - b x
--R         erf(b x)%e
--R   (21)  ----------------
--R                 4
--R                x
--R                                                    Type: Expression(Integer)
--E 51
--S 52 of 395

r0010:= -1/3*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_
        1/3*(1-2*b^2*x^2)*erf(b*x)/(exp(1)^(b^2*x^2))/x^3+_
        1/3*b^3*%pi^(1/2)*erf(b*x)^2-4/3*b^3*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R
--R   (22)
--R                              2 2
--R          2 2               2b x  +---+
--R       (2b x  - 1)erf(b x)%e     \|%pi
--R     +
--R                                                2 2    2 2          2 2
--R         3     3        2     3 3       2 2    b x   2b x          b x
--R       (b %pi x erf(b x)  - 4b x Ei(- 2b x ))%e    %e      - b x %e
--R  /
--R           2 2    2 2
--R       3  b x   2b x  +---+
--R     3x %e    %e     \|%pi
--R                                                    Type: Expression(Integer)
--E 52
--S 53 of 395
a0010:= integrate(t0010,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 53
--S 54 of 395
--m0010:= a0010-r0010
--E 54
--S 55 of 395
--d0010:= D(m0010,x)
--E 55
--S 56 of 395
t0011:= exp(1)^(-b^2*x^2)*erf(b*x)/x^2
--R
--R
--R                      2 2
--R                   - b x
--R         erf(b x)%e
--R   (23)  ----------------
--R                 2
--R                x
--R                                                    Type: Expression(Integer)

--E 56
--S 57 of 395
r0011:= -erf(b*x)/(exp(1)^(b^2*x^2))/x-1/2*b*%pi^(1/2)*erf(b*x)^2+_
        b*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R
--R                                                                        2 2
--R                     +---+                      2               2 2    b x
--R         - 2erf(b x)\|%pi  + (- b %pi x erf(b x)  + 2b x Ei(- 2b x ))%e
--R   (24)  ------------------------------------------------------------------
--R                                         2 2
--R                                        b x  +---+
--R                                   2x %e    \|%pi
--R                                                    Type: Expression(Integer)
--E 57
--S 58 of 395
a0011:= integrate(t0011,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 58
--S 59 of 395
--m0011:= a0011-r0011
--E 59
--S 60 of 395
--d0011:= D(m0011,x)
--E 60
--S 61 of 395
t0012:= x^2*exp(1)^(-b^2*x^2)*erf(b*x)
--R
--R
--R                        2 2
--R          2          - b x
--R   (25)  x erf(b x)%e
--R                                                    Type: Expression(Integer)
--E 61
--S 62 of 395
r0012:= 1/8*exp(-2*b^2*x^2)*(-2-4*x*erf(b*x)*exp(b^2*x^2)*b*%pi^(1/2)+_
        %pi*erf(b*x)^2*exp(2*b^2*x^2))/b^3/%pi^(1/2)
--R

--R
--R   (26)
--R                            2 2   2 2                            2 2    2 2
--R                        - 2b x   b x  +---+               2  - 2b x   2b x
--R       - 4b x erf(b x)%e       %e    \|%pi  + %pi erf(b x) %e       %e
--R     +
--R                2 2
--R            - 2b x
--R       - 2%e
--R  /
--R       3 +---+
--R     8b \|%pi
--R                                                    Type: Expression(Integer)
--E 62
--S 63 of 395
a0012:= integrate(t0012,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 63
--S 64 of 395
--m0012:= a0012-r0012
--E 64
--S 65 of 395
--d0012:= D(m0012,x)
--E 65
--S 66 of 395
t0013:= x^4*exp(1)^(-b^2*x^2)*erf(b*x)
--R
--R
--R                        2 2
--R          4          - b x
--R   (27)  x erf(b x)%e
--R                                                    Type: Expression(Integer)
--E 66
--S 67 of 395
r0013:= 1/16*exp(-2*b^2*x^2)*(-8-4*b^2*x^2-_
        12*x*erf(b*x)*exp(b^2*x^2)*b*%pi^(1/2)-_
        8*x^3*erf(b*x)*exp(b^2*x^2)*b^3*%pi^(1/2)+_
        3*%pi*erf(b*x)^2*exp(2*b^2*x^2))/b^5/%pi^(1/2)
--R

--R
--R   (28)
--R                                      2 2   2 2
--R            3 3                   - 2b x   b x  +---+
--R       (- 8b x  - 12b x)erf(b x)%e       %e    \|%pi
--R     +
--R                           2 2    2 2                      2 2
--R                    2  - 2b x   2b x         2 2       - 2b x
--R       3%pi erf(b x) %e       %e      + (- 4b x  - 8)%e
--R  /
--R        5 +---+
--R     16b \|%pi
--R                                                    Type: Expression(Integer)
--E 67
--S 68 of 395
a0013:= integrate(t0013,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 68
--S 69 of 395
--m0013:= a0013-r0013
--E 69
--S 70 of 395
--d0013:= D(m0013,x)
--E 70
--S 71 of 395
t0014:= x^6*exp(1)^(-b^2*x^2)*erf(b*x)
--R
--R
--R                        2 2
--R          6          - b x
--R   (29)  x erf(b x)%e
--R                                                    Type: Expression(Integer)
--E 71
--S 72 of 395
r0014:= 1/32*exp(-2*b^2*x^2)*(-44-28*b^2*x^2-8*b^4*x^4-_
        60*x*erf(b*x)*exp(b^2*x^2)*b*%pi^(1/2)-_
        40*x^3*erf(b*x)*exp(b^2*x^2)*b^3*%pi^(1/2)-_
        16*x^5*erf(b*x)*exp(b^2*x^2)*b^5*%pi^(1/2)+_
        15*%pi*erf(b*x)^2*exp(2*b^2*x^2))/b^7/%pi^(1/2)

--R
--R
--R   (30)
--R                                                2 2   2 2
--R             5 5      3 3                   - 2b x   b x  +---+
--R       (- 16b x  - 40b x  - 60b x)erf(b x)%e       %e    \|%pi
--R     +
--R                            2 2    2 2                                2 2
--R                     2  - 2b x   2b x         4 4      2 2        - 2b x
--R       15%pi erf(b x) %e       %e      + (- 8b x  - 28b x  - 44)%e
--R  /
--R        7 +---+
--R     32b \|%pi
--R                                                    Type: Expression(Integer)
--E 72
--S 73 of 395
a0014:= integrate(t0014,x)
--R
--R
--R   >> Error detected within library code:
--R   Sorry - cannot handle that integrand yet
--R
--R   Continuing to read the file...
--R
--E 73
--S 74 of 395
--m0014:= a0014-r0014
--E 74
--S 75 of 395
--d0014:= D(m0014,x)
--E 75
--S 76 of 395
t0015:= erfc(b*x)^2/x^7
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.

--E 76
--S 77 of 395
r0015:= -1/15*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^4+_
        2/9*b^4/(exp(1)^(2*b^2*x^2))/%pi/x^2+_
        2/15*b*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x^5-_
        4/45*b^3*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x^3+_
        8/45*b^5*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x-4/_
        45*b^6*erfc(b*x)^2-1/6*erfc(b*x)^2/x^6+28/45*b^6*Ei(-2*b^2*x^2)/%pi
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 77
--S 78 of 395
--a0015:= integrate(t0015,x)
--E 78
--S 79 of 395
--m0015:= a0015-r0015
--E 79
--S 80 of 395
--d0015:= D(m0015,x)
--E 80
--S 81 of 395
t0016:= erfc(b*x)^2/x^5
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,

--R      or "$" to specify which version of the function you need.
--E 81
--S 82 of 395
r0016:= -1/3*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^2+1/3*b*erfc(b*x)/_
        (exp(1)^(b^2*x^2))/%pi^(1/2)/x^3-2/3*b^3*erfc(b*x)/_
        (exp(1)^(b^2*x^2))/%pi^(1/2)/x+1/3*b^4*erfc(b*x)^2-_
        1/4*erfc(b*x)^2/x^4-4/3*b^4*Ei(-2*b^2*x^2)/%pi
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 82
--S 83 of 395
--a0016:= integrate(t0016,x)
--E 83
--S 84 of 395
--m0016:= a0016-r0016
--E 84
--S 85 of 395
--d0016:= D(m0016,x)
--E 85
--S 86 of 395
t0017:= erfc(b*x)^2/x^3
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.

--E 86
--S 87 of 395
r0017:= 2*b*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x-b^2*erfc(b*x)^2-_
        1/2*erfc(b*x)^2/x^2+2*b^2*Ei(-2*b^2*x^2)/%pi
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 87
--S 88 of 395
--a0017:= integrate(t0017,x)
--E 88
--S 89 of 395
--m0017:= a0017-r0017
--E 89
--S 90 of 395
--d0017:= D(m0017,x)
--E 90
--S 91 of 395
t0018:= erfc(b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 91
--S 92 of 395

r0018:= -2^(1/2)/%pi^(1/2)*erf(2^(1/2)*b*x)/b-2*erfc(b*x)/_
        (exp(1)^(b^2*x^2))/b/%pi^(1/2)+x*erfc(b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 92
--S 93 of 395
--a0018:= integrate(t0018,x)
--E 93
--S 94 of 395
--m0018:= a0018-r0018
--E 94
--S 95 of 395
--d0018:= D(m0018,x)
--E 95
--S 96 of 395
t0019:= x*erfc(b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 96
--S 97 of 395
r0019:= 1/2/(exp(1)^(2*b^2*x^2))/b^2/%pi-x*erfc(b*x)/_
        (exp(1)^(b^2*x^2))/b/%pi^(1/2)-1/4*erfc(b*x)^2/b^2+1/2*x^2*erfc(b*x)^2
--R

--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 97
--S 98 of 395
--a0019:= integrate(t0019,x)
--E 98
--S 99 of 395
--m0019:= a0019-r0019
--E 99
--S 100 of 395
--d0019:= D(m0019,x)
--E 100
--S 101 of 395
t0020:= x^3*erfc(b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 101
--S 102 of 395
r0020:= 1/2/(exp(1)^(2*b^2*x^2))/b^4/%pi+1/4*x^2/_
        (exp(1)^(2*b^2*x^2))/b^2/%pi-3/4*x*erfc(b*x)/_
        (exp(1)^(b^2*x^2))/b^3/%pi^(1/2)-1/2*x^3*erfc(b*x)/_
        (exp(1)^(b^2*x^2))/b/%pi^(1/2)-3/16*erfc(b*x)^2/b^4+1/4*x^4*erfc(b*x)^2
--R
--R   There are no library operations named erfc

--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 102
--S 103 of 395
--a0020:= integrate(t0020,x)
--E 103
--S 104 of 395
--m0020:= a0020-r0020
--E 104
--S 105 of 395
--d0020:= D(m0020,x)
--E 105
--S 106 of 395
t0021:= x^5*erfc(b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 106
--S 107 of 395
r0021:= 11/12/(exp(1)^(2*b^2*x^2))/b^6/%pi+7/12*x^2/_
        (exp(1)^(2*b^2*x^2))/b^4/%pi+1/6*x^4/(exp(1)^(2*b^2*x^2))/b^2/%pi-_
        5/4*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^5/%pi^(1/2)-_
        5/6*x^3*erfc(b*x)/(exp(1)^(b^2*x^2))/b^3/%pi^(1/2)-_
        1/3*x^5*erfc(b*x)/(exp(1)^(b^2*x^2))/b/%pi^(1/2)-_
        5/16*erfc(b*x)^2/b^6+1/6*x^6*erfc(b*x)^2
--R

--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 107
--S 108 of 395
--a0021:= integrate(t0021,x)
--E 108
--S 109 of 395
--m0021:= a0021-r0021
--E 109
--S 110 of 395
--d0021:= D(m0021,x)
--E 110
--S 111 of 395
t0022:= erfc(a+b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 111
--S 112 of 395
r0022:= -2^(1/2)/%pi^(1/2)*erf(2^(1/2)*(a+b*x))/b-_
        2*erfc(a+b*x)/exp((a+b*x)^2)/b/%pi^(1/2)+(a+b*x)*erfc(a+b*x)^2/b
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc

--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 112
--S 113 of 395
--a0022:= integrate(t0022,x)
--E 113
--S 114 of 395
--m0022:= a0022-r0022
--E 114
--S 115 of 395
--d0022:= D(m0022,x)
--E 115
--S 116 of 395
t0023:= x*erfc(a+b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 116
--S 117 of 395
r0023:= 1/4/b^2*(2/(exp(1)^(2*(a+b*x)^2))/%pi+4*a*2^(1/2)/%pi^(1/2)*_
        erf(2^(1/2)*(a+b*x))+erfc(a+b*x)*(4*a/exp((a+b*x)^2)/%pi^(1/2)-_
        erfc(a+b*x)-4*b*x/exp((a+b*x)^2)/%pi^(1/2)-_
        4*a*(a+b*x)*erfc(a+b*x)+2*(a+b*x)^2*erfc(a+b*x)))
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 117
--S 118 of 395
--a0023:= integrate(t0023,x)
--E 118
--S 119 of 395
--m0023:= a0023-r0023
--E 119
--S 120 of 395
--d0023:= D(m0023,x)
--E 120
--S 121 of 395
t0024:= x^2*erfc(a+b*x)^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 121
--S 122 of 395
r0024:= -1/6/b^3*(4*a/(exp(1)^(2*(a+b*x)^2))/%pi+_
        1/2*(5+12*a^2)*erf(2^(1/2)*(a+b*x))*2^(1/2)/%pi^(1/2)+_
        4*erfc(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)+_
        4*(a+b*x)^2*erfc(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)-_
        3*a*erfc(a+b*x)^2-6*a^2*(a+b*x)*erfc(a+b*x)^2+_
        6*a*(a+b*x)^2*erfc(a+b*x)^2-2*(a+b*x)^3*erfc(a+b*x)^2-_
        2*b*x*(exp(1)^(-2*(a+b*x)^2)+_
        6*a*%pi^(1/2)*erfc(a+b*x)/exp((a+b*x)^2))/%pi)
--R
--R   There are no library operations named erfc

--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 122
--S 123 of 395
--a0024:= integrate(t0024,x)
--E 123
--S 124 of 395
--m0024:= a0024-r0024
--E 124
--S 125 of 395
--d0024:= D(m0024,x)
--E 125
--S 126 of 395
t0025:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^8
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 126
--S 127 of 395
r0025:= 1/21*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^6-_
        8/105*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4+_
        4/21*b^5/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_
        1/7*erfc(b*x)/(exp(1)^(b^2*x^2))/x^7+_
        2/35*b^2*erfc(b*x)/(exp(1)^(b^2*x^2))/x^5-_
        4/105*b^4*erfc(b*x)/(exp(1)^(b^2*x^2))/x^3+_
        8/105*b^6*erfc(b*x)/(exp(1)^(b^2*x^2))/x-_

        4/105*b^7*%pi^(1/2)*erfc(b*x)^2+16/35*b^7*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 127
--S 128 of 395
--a0025:= integrate(t0025,x)
--E 128
--S 129 of 395
--m0025:= a0025-r0025
--E 129
--S 130 of 395
--d0025:= D(m0025,x)
--E 130
--S 131 of 395
t0026:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^6
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 131
--S 132 of 395
r0026:= 1/10*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4-_
        1/3*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_
        1/5*erfc(b*x)/(exp(1)^(b^2*x^2))/x^5+_
        2/15*b^2*erfc(b*x)/(exp(1)^(b^2*x^2))/x^3-_

        4/15*b^4*erfc(b*x)/(exp(1)^(b^2*x^2))/x+_
        2/15*b^5*%pi^(1/2)*erfc(b*x)^2-14/15*b^5*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 132
--S 133 of 395
--a0026:= integrate(t0026,x)
--E 133
--S 134 of 395
--m0026:= a0026-r0026
--E 134
--S 135 of 395
--d0026:= D(m0026,x)
--E 135
--S 136 of 395
t0027:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^4
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 136
--S 137 of 395
r0027:= 1/3*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_
        1/3*erfc(b*x)/(exp(1)^(b^2*x^2))/x^3+_
        2/3*b^2*erfc(b*x)/(exp(1)^(b^2*x^2))/x-_

        1/3*b^3*%pi^(1/2)*erfc(b*x)^2+4/3*b^3*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 137
--S 138 of 395
--a0027:= integrate(t0027,x)
--E 138
--S 139 of 395
--m0027:= a0027-r0027
--E 139
--S 140 of 395
--d0027:= D(m0027,x)
--E 140
--S 141 of 395
t0028:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^2
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 141
--S 142 of 395
r0028:= -erfc(b*x)/(exp(1)^(b^2*x^2))/x+_
        1/2*b*%pi^(1/2)*erfc(b*x)^2-b*Ei(-2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfc

--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 142
--S 143 of 395
--a0028:= integrate(t0028,x)
--E 143
--S 144 of 395
--m0028:= a0028-r0028
--E 144
--S 145 of 395
--d0028:= D(m0028,x)
--E 145
--S 146 of 395
t0029:= x^2*exp(1)^(-b^2*x^2)*erfc(b*x)
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 146
--S 147 of 395
r0029:= 1/4/(exp(1)^(2*b^2*x^2))/b^3/%pi^(1/2)-_
        1/2*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^2-1/8*%pi^(1/2)*erfc(b*x)^2/b^3
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 147
--S 148 of 395
--a0029:= integrate(t0029,x)
--E 148
--S 149 of 395
--m0029:= a0029-r0029
--E 149
--S 150 of 395
--d0029:= D(m0029,x)
--E 150
--S 151 of 395
t0030:= x^4*exp(1)^(-b^2*x^2)*erfc(b*x)
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 151
--S 152 of 395
r0030:= 1/2/(exp(1)^(2*b^2*x^2))/b^5/%pi^(1/2)+_
        1/4*x^2/(exp(1)^(2*b^2*x^2))/b^3/%pi^(1/2)-_
        3/4*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^4-_
        1/2*x^3*erfc(b*x)/(exp(1)^(b^2*x^2))/b^2-_
        3/16*%pi^(1/2)*erfc(b*x)^2/b^5
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 152
--S 153 of 395
--a0030:= integrate(t0030,x)
--E 153
--S 154 of 395
--m0030:= a0030-r0030
--E 154
--S 155 of 395
--d0030:= D(m0030,x)
--E 155
--S 156 of 395
t0031:= x^6*exp(1)^(-b^2*x^2)*erfc(b*x)
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue
--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 156
--S 157 of 395
r0031:= 11/8/(exp(1)^(2*b^2*x^2))/b^7/%pi^(1/2)+_
        7/8*x^2/(exp(1)^(2*b^2*x^2))/b^5/%pi^(1/2)+_
        1/4*x^4/(exp(1)^(2*b^2*x^2))/b^3/%pi^(1/2)-_
        15/8*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^6-_
        5/4*x^3*erfc(b*x)/(exp(1)^(b^2*x^2))/b^4-_
        1/2*x^5*erfc(b*x)/(exp(1)^(b^2*x^2))/b^2-_
        15/32*%pi^(1/2)*erfc(b*x)^2/b^7
--R
--R   There are no library operations named erfc
--R      Use HyperDoc Browse or issue

--R                                )what op erfc
--R      to learn if there is any operation containing " erfc " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfc
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 157
--S 158 of 395
--a0031:= integrate(t0031,x)
--E 158
--S 159 of 395
--m0031:= a0031-r0031
--E 159
--S 160 of 395
--d0031:= D(m0031,x)
--E 160
--S 161 of 395
t0032:= erfi(b*x)^2/x^7
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 161
--S 162 of 395
r0032:= -1/15*b^2*exp(1)^(2*b^2*x^2)/%pi/x^4-_
        2/9*b^4*exp(1)^(2*b^2*x^2)/%pi/x^2-_
        2/45*b*exp(1)^(b^2*x^2)*(3+2*b^2*x^2+4*b^4*x^4)*_
        erfi(b*x)/%pi^(1/2)/x^5+4/45*b^6*erfi(b*x)^2-_
        1/6*erfi(b*x)^2/x^6+28/45*b^6*Ei(2*b^2*x^2)/%pi
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue

--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 162
--S 163 of 395
--a0032:= integrate(t0032,x)
--E 163
--S 164 of 395
--m0032:= a0032-r0032
--E 164
--S 165 of 395
--d0032:= D(m0032,x)
--E 165
--S 166 of 395
t0033:= erfi(b*x)^2/x^5
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 166
--S 167 of 395
r0033:= -1/3*b^2*exp(1)^(2*b^2*x^2)/%pi/x^2-_
        1/3*b*exp(1)^(b^2*x^2)*(1+2*b^2*x^2)*erfi(b*x)/%pi^(1/2)/x^3+_
        1/3*b^4*erfi(b*x)^2-1/4*erfi(b*x)^2/x^4+4/3*b^4*Ei(2*b^2*x^2)/%pi
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 167
--S 168 of 395
--a0033:= integrate(t0033,x)
--E 168
--S 169 of 395
--m0033:= a0033-r0033
--E 169
--S 170 of 395
--d0033:= D(m0033,x)
--E 170
--S 171 of 395
t0034:= erfi(b*x)^2/x^3
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 171
--S 172 of 395
r0034:= -2*b*exp(1)^(b^2*x^2)*erfi(b*x)/%pi^(1/2)/x+_
        b^2*erfi(b*x)^2-1/2*erfi(b*x)^2/x^2+2*b^2*Ei(2*b^2*x^2)/%pi
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi

--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 172
--S 173 of 395
--a0034:= integrate(t0034,x)
--E 173
--S 174 of 395
--m0034:= a0034-r0034
--E 174
--S 175 of 395
--d0034:= D(m0034,x)
--E 175
--S 176 of 395
t0035:= erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 176
--S 177 of 395
r0035:= (-2*exp(b^2*x^2)*erfi(b*x)+x*erfi(b*x)^2*b*%pi^(1/2)+_
        2^(1/2)*erfi(2^(1/2)*b*x))/b/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R

--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 177
--S 178 of 395
--a0035:= integrate(t0035,x)
--E 178
--S 179 of 395
--m0035:= a0035-r0035
--E 179
--S 180 of 395
--d0035:= D(m0035,x)
--E 180
--S 181 of 395
t0036:= x*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 181
--S 182 of 395
r0036:= 1/2*exp(1)^(2*b^2*x^2)/b^2/%pi-_
        exp(1)^(b^2*x^2)*x*erfi(b*x)/b/%pi^(1/2)+_
        1/4*erfi(b*x)^2/b^2+1/2*x^2*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.

--E 182
--S 183 of 395
--a0036:= integrate(t0036,x)
--E 183
--S 184 of 395
--m0036:= a0036-r0036
--E 184
--S 185 of 395
--d0036:= D(m0036,x)
--E 185
--S 186 of 395
t0037:= x^2*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 186
--S 187 of 395
r0037:= 1/3*exp(1)^(2*b^2*x^2)*x/b^2/%pi+_
        2/3*exp(1)^(b^2*x^2)*(1-b^2*x^2)*erfi(b*x)/b^3/%pi^(1/2)+_
        1/3*x^3*erfi(b*x)^2-5/12*erfi(2^(1/2)*b*x)/b^3*2^(1/2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 187

--S 188 of 395
--a0037:= integrate(t0037,x)
--E 188
--S 189 of 395
--m0037:= a0037-r0037
--E 189
--S 190 of 395
--d0037:= D(m0037,x)
--E 190
--S 191 of 395
t0038:= x^3*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 191
--S 192 of 395
r0038:= -1/2*exp(1)^(2*b^2*x^2)/b^4/%pi+1/4*exp(1)^(2*b^2*x^2)*x^2/b^2/%pi+_
        1/4*exp(1)^(b^2*x^2)*x*(3-2*b^2*x^2)*erfi(b*x)/b^3/%pi^(1/2)-_
        3/16*erfi(b*x)^2/b^4+1/4*x^4*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 192
--S 193 of 395
--a0038:= integrate(t0038,x)

--E 193
--S 194 of 395
--m0038:= a0038-r0038
--E 194
--S 195 of 395
--d0038:= D(m0038,x)
--E 195
--S 196 of 395
t0039:= x^4*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 196
--S 197 of 395
r0039:= -11/20*exp(1)^(2*b^2*x^2)*x/b^4/%pi+_
        1/5*exp(1)^(2*b^2*x^2)*x^3/b^2/%pi-_
        2/5*exp(1)^(b^2*x^2)*(2-2*b^2*x^2+b^4*x^4)*erfi(b*x)/b^5/%pi^(1/2)+_
        1/5*x^5*erfi(b*x)^2+43/80*erfi(2^(1/2)*b*x)/b^5*2^(1/2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 197
--S 198 of 395
--a0039:= integrate(t0039,x)
--E 198

--S 199 of 395
--m0039:= a0039-r0039
--E 199
--S 200 of 395
--d0039:= D(m0039,x)
--E 200
--S 201 of 395
t0040:= x^5*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 201
--S 202 of 395
r0040:= 11/12*exp(1)^(2*b^2*x^2)/b^6/%pi-_
        7/12*exp(1)^(2*b^2*x^2)*x^2/b^4/%pi+_
        1/6*exp(1)^(2*b^2*x^2)*x^4/b^2/%pi-_
        1/12*exp(1)^(b^2*x^2)*x*(15-10*b^2*x^2+_
        4*b^4*x^4)*erfi(b*x)/b^5/%pi^(1/2)+5/16*erfi(b*x)^2/b^6+_
        1/6*x^6*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 202
--S 203 of 395
--a0040:= integrate(t0040,x)

--E 203
--S 204 of 395
--m0040:= a0040-r0040
--E 204
--S 205 of 395
--d0040:= D(m0040,x)
--E 205
--S 206 of 395
t0041:= x^6*erfi(b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 206
--S 207 of 395
r0041:= 21/16*exp(1)^(2*b^2*x^2)*x/b^6/%pi-_
        17/28*exp(1)^(2*b^2*x^2)*x^3/b^4/%pi+_
        1/7*exp(1)^(2*b^2*x^2)*x^5/b^2/%pi+_
        2/7*exp(1)^(b^2*x^2)*(6-6*b^2*x^2+3*b^4*x^4-_
        b^6*x^6)*erfi(b*x)/b^7/%pi^(1/2)+1/7*x^7*erfi(b*x)^2-_
        531/448*erfi(2^(1/2)*b*x)/b^7*2^(1/2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 207
--S 208 of 395

--a0041:= integrate(t0041,x)
--E 208
--S 209 of 395
--m0041:= a0041-r0041
--E 209
--S 210 of 395
--d0041:= D(m0041,x)
--E 210
--S 211 of 395
t0042:= erfi(a+b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 211
--S 212 of 395
r0042:= -2*exp((a+b*x)^2)*erfi(a+b*x)/b/%pi^(1/2)+(a+b*x)*_
        erfi(a+b*x)^2/b+2^(1/2)/%pi^(1/2)*erfi(2^(1/2)*(a+b*x))/b
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 212
--S 213 of 395
--a0042:= integrate(t0042,x)
--E 213

--S 215 of 395
--d0042:= D(m0042,x)
--E 215
--S 216 of 395
t0043:= x*erfi(a+b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 216
--S 217 of 395
r0043:= 1/4/b^2*(2*exp(1)^(2*(a+b*x)^2)/%pi+_
        4*exp((a+b*x)^2)*(a-b*x)*erfi(a+b*x)/%pi^(1/2)+_
        erfi(a+b*x)^2-4*a*(a+b*x)*erfi(a+b*x)^2+_
        2*(a+b*x)^2*erfi(a+b*x)^2-4*a*2^(1/2)/%pi^(1/2)*erfi(2^(1/2)*(a+b*x)))
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 217
--S 218 of 395
--a0043:= integrate(t0043,x)
--E 218
--S 219 of 395

--m0043:= a0043-r0043
--E 219
--S 220 of 395
--d0043:= D(m0043,x)
--E 220
--S 221 of 395
t0044:= x^2*erfi(a+b*x)^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 221
--S 222 of 395
r0044:= -1/6/b^3*(4*a*exp(1)^(2*(a+b*x)^2)/%pi-_
        2*b*exp(1)^(2*(a+b*x)^2)*x/%pi-_
        4*exp((a+b*x)^2)*(1-a^2+a*b*x-b^2*x^2)*erfi(a+b*x)/%pi^(1/2)+_
        3*a*erfi(a+b*x)^2-6*a^2*(a+b*x)*erfi(a+b*x)^2+_
        6*a*(a+b*x)^2*erfi(a+b*x)^2-2*(a+b*x)^3*erfi(a+b*x)^2+_
        1/2*(5-12*a^2)*erfi(2^(1/2)*(a+b*x))*2^(1/2)/%pi^(1/2))
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 222
--S 223 of 395
--a0044:= integrate(t0044,x)
--E 223

--S 225 of 395
--d0044:= D(m0044,x)
--E 225
--S 226 of 395
t0045:= exp(1)^(b^2*x^2)*erfi(b*x)/x^8
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 226
--S 227 of 395
r0045:= -1/21*b*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^6-_
        8/105*b^3*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^4-_
        4/21*b^5*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^2-_
        1/105*exp(1)^(b^2*x^2)*(15+6*b^2*x^2+4*b^4*x^4+_
        8*b^6*x^6)*erfi(b*x)/x^7+4/105*b^7*%pi^(1/2)*erfi(b*x)^2+_
        16/35*b^7*Ei(2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 227
--S 228 of 395
--a0045:= integrate(t0045,x)
--E 228

--S 230 of 395
--d0045:= D(m0045,x)
--E 230
--S 231 of 395
t0046:= exp(1)^(b^2*x^2)*erfi(b*x)/x^6
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 231
--S 232 of 395
r0046:= -1/10*b*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^4-_
        1/3*b^3*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^2-_
        1/15*exp(1)^(b^2*x^2)*(3+2*b^2*x^2+4*b^4*x^4)*erfi(b*x)/x^5+_
        2/15*b^5*%pi^(1/2)*erfi(b*x)^2+14/15*b^5*Ei(2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 232
--S 233 of 395
--a0046:= integrate(t0046,x)
--E 233

--S 235 of 395
--d0046:= D(m0046,x)
--E 235
--S 236 of 395
t0047:= exp(1)^(b^2*x^2)*erfi(b*x)/x^4
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 236
--S 237 of 395
r0047:= -1/3*b*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^2-_
        1/3*exp(1)^(b^2*x^2)*(1+2*b^2*x^2)*erfi(b*x)/x^3+_
        1/3*b^3*%pi^(1/2)*erfi(b*x)^2+4/3*b^3*Ei(2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 237
--S 238 of 395
--a0047:= integrate(t0047,x)
--E 238
--S 239 of 395
--m0047:= a0047-r0047

--E 239
--S 240 of 395
--d0047:= D(m0047,x)
--E 240
--S 241 of 395
t0048:= exp(1)^(b^2*x^2)*erfi(b*x)/x^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 241
--S 242 of 395
r0048:= -exp(1)^(b^2*x^2)*erfi(b*x)/x+_
        1/2*b*%pi^(1/2)*erfi(b*x)^2+b*Ei(2*b^2*x^2)/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 242
--S 243 of 395
--a0048:= integrate(t0048,x)
--E 243
--S 244 of 395
--m0048:= a0048-r0048
--E 244
--S 245 of 395

--d0048:= D(m0048,x)
--E 245
--S 246 of 395
t0049:= x*exp(1)^(b^2*x^2)*erfi(b*x)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 246
--S 247 of 395
r0049:= -1/4*(-2*exp(b^2*x^2)*erfi(b*x)+erfi(2^(1/2)*b*x)*2^(1/2))/b^2
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 247
--S 248 of 395
--a0049:= integrate(t0049,x)
--E 248
--S 249 of 395
--m0049:= a0049-r0049
--E 249
--S 250 of 395
--d0049:= D(m0049,x)
--E 250
--S 251 of 395

t0050:= x^2*exp(1)^(b^2*x^2)*erfi(b*x)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 251
--S 252 of 395
r0050:= -1/8*(2*exp(2*b^2*x^2)-4*exp(b^2*x^2)*x*erfi(b*x)*b*%pi^(1/2)+_
        %pi*erfi(b*x)^2)/b^3/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 252
--S 253 of 395
--a0050:= integrate(t0050,x)
--E 253
--S 254 of 395
--m0050:= a0050-r0050
--E 254
--S 255 of 395
--d0050:= D(m0050,x)
--E 255
--S 256 of 395
t0051:= x^3*exp(1)^(b^2*x^2)*erfi(b*x)
--R
--R   There are no library operations named erfi

--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 256
--S 257 of 395
r0051:= -1/4*exp(1)^(2*b^2*x^2)*x/b^3/%pi^(1/2)-_
        1/2*exp(1)^(b^2*x^2)*(1-b^2*x^2)*erfi(b*x)/b^4+_
        5/16*erfi(2^(1/2)*b*x)*2^(1/2)/b^4
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 257
--S 258 of 395
--a0051:= integrate(t0051,x)
--E 258
--S 259 of 395
--m0051:= a0051-r0051
--E 259
--S 260 of 395
--d0051:= D(m0051,x)
--E 260
--S 261 of 395
t0052:= x^4*exp(1)^(b^2*x^2)*erfi(b*x)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi

--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 261
--S 262 of 395
r0052:= -1/16*(-8*exp(2*b^2*x^2)+4*exp(2*b^2*x^2)*x^2*b^2+_
        12*exp(b^2*x^2)*x*erfi(b*x)*b*%pi^(1/2)-_
        8*exp(b^2*x^2)*x^3*erfi(b*x)*b^3*%pi^(1/2)-_
        3*%pi*erfi(b*x)^2)/b^5/%pi^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 262
--S 263 of 395
--a0052:= integrate(t0052,x)
--E 263
--S 264 of 395
--m0052:= a0052-r0052
--E 264
--S 265 of 395
--d0052:= D(m0052,x)
--E 265
--S 266 of 395
t0053:= x^5*exp(1)^(b^2*x^2)*erfi(b*x)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 266
--S 267 of 395
r0053:= 11/16*exp(1)^(2*b^2*x^2)*x/b^5/%pi^(1/2)-_
        1/4*exp(1)^(2*b^2*x^2)*x^3/b^3/%pi^(1/2)+_
        1/2*exp(1)^(b^2*x^2)*(2-2*b^2*x^2+b^4*x^4)*erfi(b*x)/b^6-_
        43/64*erfi(2^(1/2)*b*x)*2^(1/2)/b^6
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 267
--S 268 of 395
--a0053:= integrate(t0053,x)
--E 268
--S 269 of 395
--m0053:= a0053-r0053
--E 269
--S 270 of 395
--d0053:= D(m0053,x)
--E 270
--S 271 of 395
t0054:= x^6*exp(1)^(b^2*x^2)*erfi(b*x)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.

--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 271
--S 272 of 395
r0054:= -11/8*exp(1)^(2*b^2*x^2)/b^7/%pi^(1/2)+_
        7/8*exp(1)^(2*b^2*x^2)*x^2/b^5/%pi^(1/2)-_
        1/4*exp(1)^(2*b^2*x^2)*x^4/b^3/%pi^(1/2)+_
        1/8*exp(1)^(b^2*x^2)*x*(15-10*b^2*x^2+4*b^4*x^4)*erfi(b*x)/b^6-_
        15/32*%pi^(1/2)*erfi(b*x)^2/b^7
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 272
--S 273 of 395
--a0054:= integrate(t0054,x)
--E 273
--S 274 of 395
--m0054:= a0054-r0054
--E 274
--S 275 of 395
--d0054:= D(m0054,x)
--E 275
--S 276 of 395
t0055:= FresnelS(b*x)^2/x^9
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.

--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 276
--S 277 of 395
r0055:= -1/336*b^2/x^6+1/1680*b^6*%pi^2/x^2+1/336*b^2*cos(b^2*%pi*x^2)/x^6-_
        1/336*b^6*%pi^2*cos(b^2*%pi*x^2)/x^2+_
        1/840*b^8*%pi^4*FresnelS(b*x)^2-1/8*FresnelS(b*x)^2/x^8-_
        1/420*b*FresnelS(b*x)*(b^2*%pi*_
        x^2*(3-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)+_
        (15-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^7-_
        1/420*b^4*%pi*sin(b^2*%pi*x^2)/x^4-1/280*b^8*%pi^3*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 277
--S 278 of 395
--a0055:= integrate(t0055,x)
--E 278
--S 279 of 395
--m0055:= a0055-r0055
--E 279
--S 280 of 395
--d0055:= D(m0055,x)
--E 280
--S 281 of 395
t0056:= FresnelS(b*x)^2/x^5
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS

--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 281
--S 282 of 395
r0056:= -1/24*(b^2*x^2-b^2*cos(b^2*%pi*x^2)*x^2+2*b^4*%pi^2*_
        FresnelS(b*x)^2*x^4+6*FresnelS(b*x)^2+4*b^3*_
        FresnelS(b*x)*x^3*%pi*cos(1/2*b^2*%pi*x^2)+4*_
        FresnelS(b*x)*sin(1/2*b^2*%pi*x^2)*b*x-_
        2*b^4*%pi*Si(b^2*%pi*x^2)*x^4)/x^4
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 282
--S 283 of 395
--a0056:= integrate(t0056,x)
--E 283
--S 284 of 395
--m0056:= a0056-r0056
--E 284
--S 285 of 395
--d0056:= D(m0056,x)
--E 285
--S 286 of 395
t0057:= x^3*FresnelS(b*x)^2
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS

--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 286
--S 287 of 395
r0057:= 1/8*(3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi+_
        6*FresnelS(b*x)^2*%pi+2*x^4*FresnelS(b*x)^2*b^4*%pi^3+_
        4*x^3*FresnelS(b*x)*b^3*%pi^2*cos(1/2*b^2*%pi*x^2)-_
        12*x*FresnelS(b*x)*b*%pi*sin(1/2*b^2*%pi*x^2)-_
        4*sin(b^2*%pi*x^2))/b^4/%pi^3
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 287
--S 288 of 395
--a0057:= integrate(t0057,x)
--E 288
--S 289 of 395
--m0057:= a0057-r0057
--E 289
--S 290 of 395
--d0057:= D(m0057,x)
--E 290
--S 291 of 395
t0058:= x^7*FresnelS(b*x)^2
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS

--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 291
--S 292 of 395
r0058:= -105/16*x^2/b^6/%pi^4+7/48*x^6/b^2/%pi^2-_
        55/16*x^2*cos(b^2*%pi*x^2)/b^6/%pi^4+_
        1/16*x^6*cos(b^2*%pi*x^2)/b^2/%pi^2-_
        105/8*FresnelS(b*x)^2/b^8/%pi^4+1/8*x^8*FresnelS(b*x)^2-_
        1/4*x*FresnelS(b*x)*(b^2*%pi*x^2*(35-b^4*%pi^2*x^4)*_
        cos(1/2*b^2*%pi*x^2)-7*(15-b^4*%pi^2*x^4)*_
        sin(1/2*b^2*%pi*x^2))/b^7/%pi^4+10*sin(b^2*%pi*x^2)/b^8/%pi^5-_
        5/8*x^4*sin(b^2*%pi*x^2)/b^4/%pi^3
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 292
--S 293 of 395
--a0058:= integrate(t0058,x)
--E 293
--S 294 of 395
--m0058:= a0058-r0058
--E 294
--S 295 of 395
--d0058:= D(m0058,x)
--E 295
--S 296 of 395
t0059:= sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^8
--R

--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 296
--S 297 of 395
r0059:= -1/84*b/x^6+1/420*b^5*%pi^2/x^2+1/84*b*cos(b^2*%pi*x^2)/x^6-_
        1/84*b^5*%pi^2*cos(b^2*%pi*x^2)/x^2+1/210*b^7*%pi^4*FresnelS(b*x)^2-_
        1/105*FresnelS(b*x)*(b^2*%pi*x^2*(3-b^4*%pi^2*x^4)*_
        cos(1/2*b^2*%pi*x^2)+(15-b^4*%pi^2*x^4)*_
        sin(1/2*b^2*%pi*x^2))/x^7-1/105*b^3*%pi*_
        sin(b^2*%pi*x^2)/x^4-1/70*b^7*%pi^3*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 297
--S 298 of 395
--a0059:= integrate(t0059,x)
--E 298
--S 299 of 395
--m0059:= a0059-r0059
--E 299
--S 300 of 395
--d0059:= D(m0059,x)
--E 300
--S 301 of 395
t0060:= sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^4

--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 301
--S 302 of 395
r0060:= -1/12*(b*x-x*cos(b^2*%pi*x^2)*b+2*x^3*FresnelS(b*x)^2*b^3*%pi^2+_
        4*FresnelS(b*x)*b^2*%pi*x^2*cos(1/2*b^2*%pi*x^2)+_
        4*sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)-_
        2*b^3*%pi*Si(b^2*%pi*x^2)*x^3)/x^3
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 302
--S 303 of 395
--a0060:= integrate(t0060,x)
--E 303
--S 304 of 395
--m0060:= a0060-r0060
--E 304
--S 305 of 395
--d0060:= D(m0060,x)
--E 305
--S 306 of 395
t0061:= x^4*sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)
--R

--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 306
--S 307 of 395
r0061:= -1/4*(3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi+_
        6*FresnelS(b*x)^2*%pi+4*x^3*FresnelS(b*x)*_
        b^3*%pi^2*cos(1/2*b^2*%pi*x^2)-12*x*FresnelS(b*x)*b*%pi*_
        sin(1/2*b^2*%pi*x^2)-4*sin(b^2*%pi*x^2))/b^5/%pi^3
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 307
--S 308 of 395
--a0061:= integrate(t0061,x)
--E 308
--S 309 of 395
--m0061:= a0061-r0061
--E 309
--S 310 of 395
--d0061:= D(m0061,x)
--E 310
--S 311 of 395
t0062:= cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^10
--R
--R   There are no library operations named FresnelS

--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 311
--S 312 of 395
r0062:= 1/756*b^3*%pi/x^6-1/3780*b^7*%pi^3/x^2-_
        11/3024*b^3*%pi*cos(b^2*%pi*x^2)/x^6+_
        5/2016*b^7*%pi^3*cos(b^2*%pi*x^2)/x^2-_
        1/1890*b^9*%pi^5*FresnelS(b*x)^2-_
        1/945*FresnelS(b*x)*((105-3*b^4*%pi^2*x^4+b^8*%pi^4*x^8)*_
        cos(1/2*b^2*%pi*x^2)-b^2*%pi*x^2*(15-b^4*%pi^2*x^4)*_
        sin(1/2*b^2*%pi*x^2))/x^9-1/144*b*sin(b^2*%pi*x^2)/x^8+_
        67/30240*b^5*%pi^2*sin(b^2*%pi*x^2)/x^4+_
        83/30240*b^9*%pi^4*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 312
--S 313 of 395
--a0062:= integrate(t0062,x)
--E 313
--S 314 of 395
--m0062:= a0062-r0062
--E 314
--S 315 of 395
--d0062:= D(m0062,x)
--E 315

--S 316 of 395
t0063:= cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^6
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 316
--S 317 of 395
r0063:= 1/60*b^3*%pi/x^2-1/24*b^3*%pi*cos(b^2*%pi*x^2)/x^2+_
        1/30*b^5*%pi^3*FresnelS(b*x)^2-1/15*FresnelS(b*x)*_
        ((3-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)-b^2*%pi*x^2*_
        sin(1/2*b^2*%pi*x^2))/x^5-1/40*b*sin(b^2*%pi*x^2)/x^4-_
        7/120*b^5*%pi^2*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 317
--S 318 of 395
--a0063:= integrate(t0063,x)
--E 318
--S 319 of 395
--m0063:= a0063-r0063
--E 319
--S 320 of 395
--d0063:= D(m0063,x)
--E 320

--S 321 of 395
t0064:= cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^2
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 321
--S 322 of 395
r0064:= -cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x-_
        1/2*b*%pi*FresnelS(b*x)^2+1/4*b*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 322
--S 323 of 395
--a0064:= integrate(t0064,x)
--E 323
--S 324 of 395
--m0064:= a0064-r0064
--E 324
--S 325 of 395
--d0064:= D(m0064,x)
--E 325
--S 326 of 395
t0065:= x^2*cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)
--R

--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 326
--S 327 of 395
r0065:= 1/4*(-b^2*%pi*x^2-2*FresnelS(b*x)^2*%pi+_
        4*x*FresnelS(b*x)*b*%pi*sin(1/2*b^2*%pi*x^2)+_
        sin(b^2*%pi*x^2))/b^3/%pi^2
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 327
--S 328 of 395
--a0065:= integrate(t0065,x)
--E 328
--S 329 of 395
--m0065:= a0065-r0065
--E 329
--S 330 of 395
--d0065:= D(m0065,x)
--E 330
--S 331 of 395
t0066:= x^6*cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue

--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 331
--S 332 of 395
r0066:= 1/12*(45*b^2*%pi*x^2-x^6*b^6*%pi^3+_
        21*x^2*cos(b^2*%pi*x^2)*b^2*%pi+90*FresnelS(b*x)^2*%pi+_
        60*x^3*FresnelS(b*x)*b^3*%pi^2*cos(1/2*b^2*%pi*x^2)-_
        180*x*FresnelS(b*x)*b*%pi*sin(1/2*b^2*%pi*x^2)+_
        12*x^5*FresnelS(b*x)*b^5*%pi^3*sin(1/2*b^2*%pi*x^2)-_
        66*sin(b^2*%pi*x^2)+3*x^4*sin(b^2*%pi*x^2)*b^4*%pi^2)/b^7/%pi^4
--R
--R   There are no library operations named FresnelS
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelS
--R      to learn if there is any operation containing " FresnelS " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelS with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 332
--S 333 of 395
--a0066:= integrate(t0066,x)
--E 333
--S 334 of 395
--m0066:= a0066-r0066
--E 334
--S 335 of 395
--d0066:= D(m0066,x)
--E 335
--S 336 of 395
t0067:= FresnelC(b*x)^2/x^9
--R
--R   There are no library operations named FresnelC

--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 336
--S 337 of 395
r0067:= -1/336*b^2/x^6+1/1680*b^6*%pi^2/x^2-_
        1/336*b^2*cos(b^2*%pi*x^2)/x^6+1/336*b^6*%pi^2*cos(b^2*%pi*x^2)/x^2+_
        1/840*b^8*%pi^4*FresnelC(b*x)^2-1/8*FresnelC(b*x)^2/x^8-_
        1/420*b*FresnelC(b*x)*((15-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)-_
        b^2*%pi*x^2*(3-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^7+_
        1/420*b^4*%pi*sin(b^2*%pi*x^2)/x^4+1/280*b^8*%pi^3*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 337
--S 338 of 395
--a0067:= integrate(t0067,x)
--E 338
--S 339 of 395
--m0067:= a0067-r0067
--E 339
--S 340 of 395
--d0067:= D(m0067,x)
--E 340
--S 341 of 395
t0068:= FresnelC(b*x)^2/x^5
--R

--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 341
--S 342 of 395
r0068:= -1/24*(b^2*x^2+b^2*cos(b^2*%pi*x^2)*x^2+2*b^4*%pi^2*_
        FresnelC(b*x)^2*x^4+6*FresnelC(b*x)^2+4*FresnelC(b*x)*_
        cos(1/2*b^2*%pi*x^2)*b*x-4*b^3*FresnelC(b*x)*x^3*%pi*_
        sin(1/2*b^2*%pi*x^2)+2*b^4*%pi*Si(b^2*%pi*x^2)*x^4)/x^4
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 342
--S 343 of 395
--a0068:= integrate(t0068,x)
--E 343
--S 344 of 395
--m0068:= a0068-r0068
--E 344
--S 345 of 395
--d0068:= D(m0068,x)
--E 345
--S 346 of 395
t0069:= x^3*FresnelC(b*x)^2
--R
--R   There are no library operations named FresnelC

--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 346
--S 347 of 395
r0069:= -1/8*(-3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi-_
        6*FresnelC(b*x)^2*%pi-2*x^4*FresnelC(b*x)^2*b^4*%pi^3+_
        12*x*FresnelC(b*x)*b*%pi*cos(1/2*b^2*%pi*x^2)+_
        4*x^3*FresnelC(b*x)*b^3*%pi^2*sin(1/2*b^2*%pi*x^2)-_
        4*sin(b^2*%pi*x^2))/b^4/%pi^3
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 347
--S 348 of 395
--a0069:= integrate(t0069,x)
--E 348
--S 349 of 395
--m0069:= a0069-r0069
--E 349
--S 350 of 395
--d0069:= D(m0069,x)
--E 350
--S 351 of 395
t0070:= x^7*FresnelC(b*x)^2
--R
--R   There are no library operations named FresnelC

--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 351
--S 352 of 395
r0070:= -105/16*x^2/b^6/%pi^4+7/48*x^6/b^2/%pi^2+_
        55/16*x^2*cos(b^2*%pi*x^2)/b^6/%pi^4-_
        1/16*x^6*cos(b^2*%pi*x^2)/b^2/%pi^2-105/8*FresnelC(b*x)^2/b^8/%pi^4+_
        1/8*x^8*FresnelC(b*x)^2+1/4*x*FresnelC(b*x)*_
        (7*(15-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)+_
        b^2*%pi*x^2*(35-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/b^7/%pi^4-_
        10*sin(b^2*%pi*x^2)/b^8/%pi^5+5/8*x^4*sin(b^2*%pi*x^2)/b^4/%pi^3
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 352
--S 353 of 395
--a0070:= integrate(t0070,x)
--E 353
--S 354 of 395
--m0070:= a0070-r0070
--E 354
--S 355 of 395
--d0070:= D(m0070,x)
--E 355
--S 356 of 395
t0071:= sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^10

--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 356
--S 357 of 395
r0071:= -1/756*b^3*%pi/x^6+1/3780*b^7*%pi^3/x^2-_
        11/3024*b^3*%pi*cos(b^2*%pi*x^2)/x^6+_
        5/2016*b^7*%pi^3*cos(b^2*%pi*x^2)/x^2+_
        1/1890*b^9*%pi^5*FresnelC(b*x)^2-_
        1/945*FresnelC(b*x)*(b^2*%pi*x^2*(15-b^4*%pi^2*x^4)*_
        cos(1/2*b^2*%pi*x^2)+(105-3*b^4*%pi^2*x^4+b^8*%pi^4*x^8)*_
        sin(1/2*b^2*%pi*x^2))/x^9-1/144*b*sin(b^2*%pi*x^2)/x^8+_
        67/30240*b^5*%pi^2*sin(b^2*%pi*x^2)/x^4+83/30240*_
        b^9*%pi^4*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 357
--S 358 of 395
--a0071:= integrate(t0071,x)
--E 358
--S 359 of 395
--m0071:= a0071-r0071
--E 359
--S 360 of 395
--d0071:= D(m0071,x)

--E 360
--S 361 of 395
t0072:= sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^6
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 361
--S 362 of 395
r0072:= -1/60*b^3*%pi/x^2-1/24*b^3*%pi*cos(b^2*%pi*x^2)/x^2-_
        1/30*b^5*%pi^3*FresnelC(b*x)^2-_
        1/15*FresnelC(b*x)*(b^2*%pi*x^2*cos(1/2*b^2*%pi*x^2)+_
        (3-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^5-_
        1/40*b*sin(b^2*%pi*x^2)/x^4-7/120*b^5*%pi^2*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 362
--S 363 of 395
--a0072:= integrate(t0072,x)
--E 363
--S 364 of 395
--m0072:= a0072-r0072
--E 364
--S 365 of 395
--d0072:= D(m0072,x)

--E 365
--S 366 of 395
t0073:= sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^2
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 366
--S 367 of 395
r0073:= 1/2*b*%pi*FresnelC(b*x)^2-FresnelC(b*x)*sin(1/2*b^2*%pi*x^2)/x+_
        1/4*b*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 367
--S 368 of 395
--a0073:= integrate(t0073,x)
--E 368
--S 369 of 395
--m0073:= a0073-r0073
--E 369
--S 370 of 395
--d0073:= D(m0073,x)
--E 370
--S 371 of 395

t0074:= x^2*sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 371
--S 372 of 395
r0074:= -1/4*(-b^2*%pi*x^2+4*x*FresnelC(b*x)*b*%pi*cos(1/2*b^2*%pi*x^2)-_
        2*FresnelC(b*x)^2*%pi-sin(b^2*%pi*x^2))/b^3/%pi^2
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 372
--S 373 of 395
--a0074:= integrate(t0074,x)
--E 373
--S 374 of 395
--m0074:= a0074-r0074
--E 374
--S 375 of 395
--d0074:= D(m0074,x)
--E 375
--S 376 of 395
t0075:= x^6*sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)
--R
--R   There are no library operations named FresnelC

--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 376
--S 377 of 395
r0075:= -1/12*(45*b^2*%pi*x^2-x^6*b^6*%pi^3-21*x^2*cos(b^2*%pi*x^2)*b^2*%pi+_
        90*FresnelC(b*x)^2*%pi-180*x*FresnelC(b*x)*b*_
        %pi*cos(1/2*b^2*%pi*x^2)+12*x^5*FresnelC(b*x)*b^5*%pi^3*_
        cos(1/2*b^2*%pi*x^2)-60*x^3*FresnelC(b*x)*b^3*%pi^2*_
        sin(1/2*b^2*%pi*x^2)+66*sin(b^2*%pi*x^2)-_
        3*x^4*sin(b^2*%pi*x^2)*b^4*%pi^2)/b^7/%pi^4
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 377
--S 378 of 395
--a0075:= integrate(t0075,x)
--E 378
--S 379 of 395
--m0075:= a0075-r0075
--E 379
--S 380 of 395
--d0075:= D(m0075,x)
--E 380
--S 381 of 395
t0076:= cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^8
--R

--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 381
--S 382 of 395
r0076:= -1/84*b/x^6+1/420*b^5*%pi^2/x^2-1/84*b*cos(b^2*%pi*x^2)/x^6+_
        1/84*b^5*%pi^2*cos(b^2*%pi*x^2)/x^2+1/210*b^7*%pi^4*FresnelC(b*x)^2-_
        1/105*FresnelC(b*x)*((15-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)-_
        b^2*%pi*x^2*(3-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^7+_
        1/105*b^3*%pi*sin(b^2*%pi*x^2)/x^4+1/70*b^7*%pi^3*Si(b^2*%pi*x^2)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 382
--S 383 of 395
--a0076:= integrate(t0076,x)
--E 383
--S 384 of 395
--m0076:= a0076-r0076
--E 384
--S 385 of 395
--d0076:= D(m0076,x)
--E 385
--S 386 of 395
t0077:= cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^4
--R

--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 386
--S 387 of 395
r0077:= -1/12*(b*x+x*cos(b^2*%pi*x^2)*b+2*x^3*FresnelC(b*x)^2*b^3*%pi^2+_
        4*cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)-4*FresnelC(b*x)*b^2*%pi*x^2*_
        sin(1/2*b^2*%pi*x^2)+2*b^3*%pi*Si(b^2*%pi*x^2)*x^3)/x^3
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 387
--S 388 of 395
--a0077:= integrate(t0077,x)
--E 388
--S 389 of 395
--m0077:= a0077-r0077
--E 389
--S 390 of 395
--d0077:= D(m0077,x)
--E 390
--S 391 of 395
t0078:= x^4*cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue

--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 391
--S 392 of 395
r0078:= 1/4*(-3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi-_
        6*FresnelC(b*x)^2*%pi+12*x*FresnelC(b*x)*b*%pi*_
        cos(1/2*b^2*%pi*x^2)+4*x^3*FresnelC(b*x)*_
        b^3*%pi^2*sin(1/2*b^2*%pi*x^2)-4*sin(b^2*%pi*x^2))/b^5/%pi^3
--R
--R   There are no library operations named FresnelC
--R      Use HyperDoc Browse or issue
--R                              )what op FresnelC
--R      to learn if there is any operation containing " FresnelC " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      FresnelC with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 392
--S 393 of 395
--a0078:= integrate(t0078,x)
--E 393
--S 394 of 395
--m0078:= a0078-r0078
--E 394
--S 395 of 395
--d0078:= D(m0078,x)
--E 395
)spool

———-

References

[1] Rich, Albert D. “Rule-based Mathematics” www.apmaths.uwo.ca/~arich