$SPAD/src/input richspecfunc000-022.input

Albert Rich and Timothy Daly December 3, 2016

Abstract

Contents

2

— * —

)set break resume
)sys rm -f richspecfunc000-022.output
)spool richspecfunc000-022.output
)set message auto off
)clear all
--S 1 of 115
t0000:= Gamma(n,a+b*x)
--R
--R
--R         _
--R   (1)  | (n,b x + a)
--R                                                    Type: Expression(Integer)
--E 1
--S 2 of 115
r0000:= (a+b*x)*Gamma(n,a+b*x)/b-Gamma(1+n,a+b*x)/b
--R
--R
--R           __
--R        - | (n + 1,b x + a) + (b x + a)| (n,b x + a)
--R   (2)  --------------------------------------------
--R                              b
--R                                                    Type: Expression(Integer)
--E 2
--S 3 of 115
a0000:= integrate(t0000,x)
--R
--R
--R           x
--R         ++   _
--R   (3)   |   | (n,%K b + a)d%K
--R        ++
--R                                         Type: Union(Expression(Integer),...)
--E 3
--S 4 of 115
--m0000:= a0000-r0000
--E 4
--S 5 of 115
--d0000:= D(m0000,x)
--E 5
--S 6 of 115
t0001:= x*Gamma(n,a+b*x)

--R
--R
--R          _
--R   (4)  x| (n,b x + a)
--R                                                    Type: Expression(Integer)
--E 6
--S 7 of 115
r0001:= -1/2*(a^2/b^2-x^2)*Gamma(n,a+b*x)+a*Gamma(1+n,a+b*x)/b^2-1/2*_
        Gamma(2+n,a+b*x)/b^2
--R
--R
--R           __2 2    2  _
--R        - | (n + 2,b x + a) + 2a| (n + 1,b x + a) + (b x  - a )| (n,b x + a)
--R   (5)  --------------------------------------------------------------------
--R                                           2
--R                                         2b
--R                                                    Type: Expression(Integer)
--E 7
--S 8 of 115
a0001:= integrate(t0001,x)
--R
--R
--R           x
--R         ++     _
--R   (6)   |   %K| (n,%K b + a)d%K
--R        ++
--R                                         Type: Union(Expression(Integer),...)
--E 8
--S 9 of 115
--m0001:= a0001-r0001
--E 9
--S 10 of 115
--d0001:= D(m0001,x)
--E 10
--S 11 of 115
t0002:= x^2*Gamma(n,a+b*x)
--R
--R
--R         2 _
--R   (7)  x | (n,b x + a)
--R                                                    Type: Expression(Integer)
--E 11
--S 12 of 115
r0002:= -1/3*(-Gamma(n,a+b*x)*a^3-Gamma(n,a+b*x)*b^3*x^3+3*a^2*_

        Gamma(1+n,a+b*x)-3*a*Gamma(2+n,a+b*x)+Gamma(3+n,a+b*x))/b^3
--R
--R
--R   (8)
--R          __2 _
--R       - | (n + 3,b x + a) + 3a| (n + 2,b x + a) - 3a | (n + 1,b x + a)
--R     +
--R         3 3    3  _
--R       (b x  + a )| (n,b x + a)
--R  /
--R       3
--R     3b
--R                                                    Type: Expression(Integer)
--E 12
--S 13 of 115
a0002:= integrate(t0002,x)
--R
--R
--R           x
--R         ++    2 _
--R   (9)   |   %K | (n,%K b + a)d%K
--R        ++
--R                                         Type: Union(Expression(Integer),...)
--E 13
--S 14 of 115
--m0002:= a0002-r0002
--E 14
--S 15 of 115
--d0002:= D(m0002,x)
--E 15
--S 16 of 115
t0003:= log(Gamma(a+b*x))
--R
--R
--R              _
--R   (10)  log(| (b x + a))
--R                                                    Type: Expression(Integer)
--E 16
--S 17 of 115
r0003:= x*log(Gamma(a+b*x))-x*logGamma(a+b*x)+Psi(-2,a+b*x)/b
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma

--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named
--R      logGamma 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 17
--S 18 of 115
a0003:= integrate(t0003,x)
--R
--R
--R            x
--R          ++       _
--R   (11)   |   log(| (%K b + a))d%K
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 18
--S 19 of 115
--m0003:= a0003-r0003
--E 19
--S 20 of 115
--d0003:= D(m0003,x)
--E 20
--S 21 of 115
t0004:= x*log(Gamma(a+b*x))
--R
--R
--R                _
--R   (12)  x log(| (b x + a))
--R                                                    Type: Expression(Integer)
--E 21
--S 22 of 115
r0004:= 1/2*x^2*log(Gamma(a+b*x))-1/2*x^2*logGamma(a+b*x)-_
        Psi(-3,a+b*x)/b^2+x*Psi(-2,a+b*x)/b
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments

--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named
--R      logGamma 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 22
--S 23 of 115
a0004:= integrate(t0004,x)
--R
--R
--R            x
--R          ++          _
--R   (13)   |   %K log(| (%K b + a))d%K
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 23
--S 24 of 115
--m0004:= a0004-r0004
--E 24
--S 25 of 115
--d0004:= D(m0004,x)
--E 25
--S 26 of 115
t0005:= x^2*log(Gamma(a+b*x))
--R
--R
--R          2     _
--R   (14)  x log(| (b x + a))
--R                                                    Type: Expression(Integer)
--E 26
--S 27 of 115
r0005:= 1/3*x^3*log(Gamma(a+b*x))-1/3*x^3*logGamma(a+b*x)+2*_
        Psi(-4,a+b*x)/b^3-2*x*Psi(-3,a+b*x)/b^2+x^2*Psi(-2,a+b*x)/b
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R

--R   Cannot find a definition or applicable library operation named
--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 27
--S 28 of 115
a0005:= integrate(t0005,x)
--R
--R
--R            x
--R          ++    2     _
--R   (15)   |   %K log(| (%K b + a))d%K
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 28
--S 29 of 115
--m0005:= a0005-r0005
--E 29
--S 30 of 115
--d0005:= D(m0005,x)
--E 30
--S 31 of 115
t0006:= logGamma(a+b*x)
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named
--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 31
--S 32 of 115
r0006:= Psi(-2,a+b*x)/b
--R
--R   There are no library operations named Psi

--R      Use HyperDoc Browse or issue
--R                                )what op Psi
--R      to learn if there is any operation containing " Psi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Psi
--R      with argument type(s)
--R                                   Integer
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 32
--S 33 of 115
--a0006:= integrate(t0006,x)
--E 33
--S 34 of 115
--m0006:= a0006-r0006
--E 34
--S 35 of 115
--d0006:= D(m0006,x)
--E 35
--S 36 of 115
t0007:= x*logGamma(a+b*x)
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named
--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 36
--S 37 of 115
r0007:= -(Psi(-3,a+b*x)-x*Psi(-2,a+b*x)*b)/b^2
--R
--R   There are no library operations named Psi
--R      Use HyperDoc Browse or issue

--R                                )what op Psi
--R      to learn if there is any operation containing " Psi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Psi
--R      with argument type(s)
--R                                   Integer
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 37
--S 38 of 115
--a0007:= integrate(t0007,x)
--E 38
--S 39 of 115
--m0007:= a0007-r0007
--E 39
--S 40 of 115
--d0007:= D(m0007,x)
--E 40
--S 41 of 115
t0008:= x^2*logGamma(a+b*x)
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named
--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 41
--S 42 of 115
r0008:= 2*Psi(-4,a+b*x)/b^3-2*x*Psi(-3,a+b*x)/b^2+x^2*Psi(-2,a+b*x)/b
--R
--R   There are no library operations named Psi
--R      Use HyperDoc Browse or issue
--R                                )what op Psi

--R      to learn if there is any operation containing " Psi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Psi
--R      with argument type(s)
--R                                   Integer
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 42
--S 43 of 115
--a0008:= integrate(t0008,x)
--E 43
--S 44 of 115
--m0008:= a0008-r0008
--E 44
--S 45 of 115
--d0008:= D(m0008,x)
--E 45
--S 46 of 115
t0009:= x*Psi(n,a+b*x)
--R
--R   There are no library operations named Psi
--R      Use HyperDoc Browse or issue
--R                                )what op Psi
--R      to learn if there is any operation containing " Psi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Psi
--R      with argument type(s)
--R                                 Variable(n)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 46
--S 47 of 115
r0009:= (-Psi(-2+n,a+b*x)+x*Psi(-1+n,a+b*x)*b)/b^2
--R
--R   There are no library operations named Psi
--R      Use HyperDoc Browse or issue
--R                                )what op Psi
--R      to learn if there is any operation containing " Psi " in its
--R      name.

--R
--R   Cannot find a definition or applicable library operation named Psi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 47
--S 48 of 115
--a0009:= integrate(t0009,x)
--E 48
--S 49 of 115
--m0009:= a0009-r0009
--E 49
--S 50 of 115
--d0009:= D(m0009,x)
--E 50
--S 51 of 115
t0010:= x^2*Psi(1,a+b*x)
--R
--R   There are no library operations named Psi
--R      Use HyperDoc Browse or issue
--R                                )what op Psi
--R      to learn if there is any operation containing " Psi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Psi
--R      with argument type(s)
--R                               PositiveInteger
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 51
--S 52 of 115
r0010:= (-2*x*logGamma(a+b*x)*b+2*Psi(-2,a+b*x)+x^2*Psi(a+b*x)*b^2)/b^3
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.

--R
--R   Cannot find a definition or applicable library operation named
--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 52
--S 53 of 115
--a0010:= integrate(t0010,x)
--E 53
--S 54 of 115
--m0010:= a0010-r0010
--E 54
--S 55 of 115
--d0010:= D(m0010,x)
--E 55
--S 56 of 115
t0011:= x*Zeta(2,a+b*x)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                               PositiveInteger
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 56
--S 57 of 115
r0011:= (-logGamma(a+b*x)+x*Psi(a+b*x)*b)/b^2
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R

--R   Cannot find a definition or applicable library operation named
--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 57
--S 58 of 115
--a0011:= integrate(t0011,x)
--E 58
--S 59 of 115
--m0011:= a0011-r0011
--E 59
--S 60 of 115
--d0011:= D(m0011,x)
--E 60
--S 61 of 115
t0012:= x^2*Zeta(2,a+b*x)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                               PositiveInteger
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 61
--S 62 of 115
r0012:= (-2*x*logGamma(a+b*x)*b+2*Psi(-2,a+b*x)+x^2*Psi(a+b*x)*b^2)/b^3
--R
--R   There are 2 exposed and 0 unexposed library operations named
--R      logGamma having 1 argument(s) but none was determined to be
--R      applicable. Use HyperDoc Browse, or issue
--R                            )display op logGamma
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named

--R      logGamma with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 62
--S 63 of 115
--a0012:= integrate(t0012,x)
--E 63
--S 64 of 115
--m0012:= a0012-r0012
--E 64
--S 65 of 115
--d0012:= D(m0012,x)
--E 65
--S 66 of 115
t0013:= Zeta(s,a+b*x)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                                 Variable(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 66
--S 67 of 115
r0013:= -Zeta(-1+s,a+b*x)/b/(-1+s)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                             Polynomial(Integer)
--R                             Polynomial(Integer)

--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 67
--S 68 of 115
--a0013:= integrate(t0013,x)
--E 68
--S 69 of 115
--m0013:= a0013-r0013
--E 69
--S 70 of 115
--d0013:= D(m0013,x)
--E 70
--S 71 of 115
t0014:= x*Zeta(s,a+b*x)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                                 Variable(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 71
--S 72 of 115
r0014:= -Zeta(-2+s,a+b*x)/b^2/(1-s)/(2-s)+x*Zeta(-1+s,a+b*x)/b/(1-s)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                             Polynomial(Integer)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,

--R      or "$" to specify which version of the function you need.
--E 72
--S 73 of 115
--a0014:= integrate(t0014,x)
--E 73
--S 74 of 115
--m0014:= a0014-r0014
--E 74
--S 75 of 115
--d0014:= D(m0014,x)
--E 75
--S 76 of 115
t0015:= x^2*Zeta(s,a+b*x)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                                 Variable(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 76
--S 77 of 115
r0015:= 2*Zeta(-3+s,a+b*x)/b^3/(1-s)/(2-s)/(3-s)-_
        2*x*Zeta(-2+s,a+b*x)/b^2/(1-s)/(2-s)+x^2*Zeta(-1+s,a+b*x)/b/(1-s)
--R
--R   There are no library operations named Zeta
--R      Use HyperDoc Browse or issue
--R                                )what op Zeta
--R      to learn if there is any operation containing " Zeta " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named Zeta
--R      with argument type(s)
--R                             Polynomial(Integer)
--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 115
--a0015:= integrate(t0015,x)
--E 78
--S 79 of 115
--m0015:= a0015-r0015
--E 79
--S 80 of 115
--d0015:= D(m0015,x)
--E 80
--S 81 of 115
t0016:= polylog(n,a*x^m)/x
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                                 Variable(n)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 81
--S 82 of 115
r0016:= polylog(1+n,a*x^m)/m
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                             Polynomial(Integer)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 82

--S 83 of 115
--a0016:= integrate(t0016,x)
--E 83
--S 84 of 115
--m0016:= a0016-r0016
--E 84
--S 85 of 115
--d0016:= D(m0016,x)
--E 85
--S 86 of 115
t0017:= polylog(2,a+b*x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 86
--S 87 of 115
r0017:= -x-(1-a-b*x)*log(1-a-b*x)/b+(x+a/b)*polylog(2,a+b*x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 87
--S 88 of 115
--a0017:= integrate(t0017,x)

--E 88
--S 89 of 115
--m0017:= a0017-r0017
--E 89
--S 90 of 115
--d0017:= D(m0017,x)
--E 90
--S 91 of 115
t0018:= polylog(n,a*f^x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                                 Variable(n)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 91
--S 92 of 115
r0018:= polylog(1+n,a*f^x)/log(f)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                             Polynomial(Integer)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 92
--S 93 of 115
--a0018:= integrate(t0018,x)
--E 93

--S 94 of 115
--m0018:= a0018-r0018
--E 94
--S 95 of 115
--d0018:= D(m0018,x)
--E 95
--S 96 of 115
t0019:= x*polylog(n,a*f^x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                                 Variable(n)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 96
--S 97 of 115
r0019:= 1/log(f)^2*(x*polylog(1+n,a*f^x)*log(f)-polylog(2+n,a*f^x))
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                             Polynomial(Integer)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 97
--S 98 of 115
--a0019:= integrate(t0019,x)
--E 98
--S 99 of 115
--m0019:= a0019-r0019

--E 99
--S 100 of 115
--d0019:= D(m0019,x)
--E 100
--S 101 of 115
t0020:= x^2*polylog(n,a*f^x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                                 Variable(n)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 101
--S 102 of 115
r0020:= 1/log(f)^3*(x^2*polylog(1+n,a*f^x)*log(f)^2-_
        2*x*polylog(2+n,a*f^x)*log(f)+2*polylog(3+n,a*f^x))
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                             Polynomial(Integer)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 102
--S 103 of 115
--a0020:= integrate(t0020,x)
--E 103
--S 104 of 115
--m0020:= a0020-r0020
--E 104

--S 105 of 115
--d0020:= D(m0020,x)
--E 105
--S 106 of 115
t0021:= log(x)*polylog(n,a*x)/x
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                                 Variable(n)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 106
--S 107 of 115
r0021:= log(x)*polylog(1+n,a*x)-polylog(2+n,a*x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                             Polynomial(Integer)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 107
--S 108 of 115
--a0021:= integrate(t0021,x)
--E 108
--S 109 of 115
--m0021:= a0021-r0021
--E 109
--S 110 of 115

--d0021:= D(m0021,x)
--E 110
--S 111 of 115
t0022:= log(x)^2*polylog(n,a*x)/x
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                                 Variable(n)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 111
--S 112 of 115
r0022:= log(x)^2*polylog(1+n,a*x)-2*log(x)*polylog(2+n,a*x)+2*polylog(3+n,a*x)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                             Polynomial(Integer)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 112
--S 113 of 115
--a0022:= integrate(t0022,x)
--E 113
--S 114 of 115
--m0022:= a0022-r0022
--E 114
--S 115 of 115
--d0022:= D(m0022,x)
--E 115

)spool  ———-

25

References

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