$SPAD/src/input besselk.input

Timothy Daly December 3, 2016

Abstract

Contents

2

In the following table there are 4 columns. The first column is the argument of besselK, ranging from 0.01 to 10.0. The second column is the reference value of Gamma from the book Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp417-419

— * —

)set break resume
)spool besselk.output
)set message test on
)set message auto off
)clear all
--S 1 of 6
D(besselK(a,x),x)
--R
--R        - besselK(a + 1,x) - besselK(a - 1,x)
--R   (1)  -------------------------------------
--R                          2
--R                                                    Type: Expression(Integer)
--E 1
--S 2 of 6
D(besselK(a,x),a)
--R
--R   (2)  besselK  (a,x)
--R               ,1
--R                                                    Type: Expression(Integer)
--E 2
--S 3 of 6
integrate(D(besselK(a,x),a),a)
--R
--R   (3)  besselK(a,x)
--R                                         Type: Union(Expression(Integer),...)
--E 3
--S 4 of 6
limit(D(besselK(a,x),a),a=1/2)
--R
--R   (4)  "failed"
--R                                                    Type: Union("failed",...)
--E 4
--S 5 of 6
stegun(x)== %e^x * besselK(1,x)
--E 5
--S 6 of 6
[[0.1, 10.890182683 , stegun(0.1),  stegun(0.1)- 10.890182683 ],_
 [0.2,  5.833386037 , stegun(0.2),  stegun(0.2)-  5.833386037 ],_

[0.3,  4.125157762 , stegun(0.3),  stegun(0.3)-  4.125157762 ],_
[0.4,  3.258673880 , stegun(0.4),  stegun(0.4)-  3.258673880 ],_
[0.5,  2.7310097082, stegun(0.5),  stegun(0.5)-  2.7310097082],_
[0.6,  2.3739200376, stegun(0.6),  stegun(0.6)-  2.3739200376],_
[0.7,  2.1150113128, stegun(0.7),  stegun(0.7)-  2.1150113128],_
[0.8,  1.9179302990, stegun(0.8),  stegun(0.8)-  1.9179302990],_
[0.9,  1.7623882197, stegun(0.9),  stegun(0.9)-  1.7623882197],_
[1.0,  1.6361534863, stegun(1.0),  stegun(1.0)-  1.6361534863],_
[1.1,  1.5314037541, stegun(1.1),  stegun(1.1)-  1.5314037541],_
[1.2,  1.4428975522, stegun(1.2),  stegun(1.2)-  1.4428975522],_
[1.3,  1.3669872841, stegun(1.3),  stegun(1.3)-  1.3669872841],_
[1.4,  1.3010537400, stegun(1.4),  stegun(1.4)-  1.3010537400],_
[1.5,  1.2431658736, stegun(1.5),  stegun(1.5)-  1.2431658736],_
[1.6,  1.1918675654, stegun(1.6),  stegun(1.6)-  1.1918675654],_
[1.7,  1.1460392462, stegun(1.7),  stegun(1.7)-  1.1460392462],_
[1.8,  1.1048053726, stegun(1.8),  stegun(1.8)-  1.1048053726],_
[1.9,  1.0674709298, stegun(1.9),  stegun(1.9)-  1.0674709298],_
[2.0,  1.0334768471, stegun(2.0),  stegun(2.0)-  1.0334768471],_
[2.1,  1.0023680527, stegun(2.1),  stegun(2.1)-  1.0023680527],_
[2.2,  0.9737701679, stegun(2.2),  stegun(2.2)-  0.9737701679],_
[2.3,  0.9473722250, stegun(2.3),  stegun(2.3)-  0.9473722250],_
[2.4,  0.9229136650, stegun(2.4),  stegun(2.4)-  0.9229136650],_
[2.5,  0.9001744239, stegun(2.5),  stegun(2.5)-  0.9001744239],_
[2.6,  0.8789672806, stegun(2.6),  stegun(2.6)-  0.8789672806],_
[2.7,  0.8591318867, stegun(2.7),  stegun(2.7)-  0.8591318867],_
[2.8,  0.8405300604, stegun(2.8),  stegun(2.8)-  0.8405300604],_
[2.9,  0.8230420403, stegun(2.9),  stegun(2.9)-  0.8230420403],_
[3.0,  0.8065634800, stegun(3.0),  stegun(3.0)-  0.8065634800],_
[3.1,  0.7910030157, stegun(3.1),  stegun(3.1)-  0.7910030157],_
[3.2,  0.7762802824, stegun(3.2),  stegun(3.2)-  0.7762802824],_
[3.3,  0.7623242864, stegun(3.3),  stegun(3.3)-  0.7623242864],_
[3.4,  0.7490720613, stegun(3.4),  stegun(3.4)-  0.7490720613],_
[3.5,  0.7364675480, stegun(3.5),  stegun(3.5)-  0.7364675480],_
[3.6,  0.7244606608, stegun(3.6),  stegun(3.6)-  0.7244606608],_
[3.7,  0.7130065010, stegun(3.7),  stegun(3.7)-  0.7130065010],_
[3.8,  0.7020646931, stegun(3.8),  stegun(3.8)-  0.7020646931],_
[3.9,  0.6915988206, stegun(3.9),  stegun(3.9)-  0.6915988206],_
[4.0,  0.6815759452, stegun(4.0),  stegun(4.0)-  0.6815759452],_
[4.1,  0.6719661952, stegun(4.1),  stegun(4.1)-  0.6719661952],_
[4.2,  0.6627424110, stegun(4.2),  stegun(4.2)-  0.6627424110],_
[4.3,  0.6538798395, stegun(4.3),  stegun(4.3)-  0.6538798395],_
[4.4,  0.6453558689, stegun(4.4),  stegun(4.4)-  0.6453558689],_
[4.5,  0.6371497988, stegun(4.5),  stegun(4.5)-  0.6371497988],_
[4.6,  0.6292426383, stegun(4.6),  stegun(4.6)-  0.6292426383],_
[4.7,  0.6216169312, stegun(4.7),  stegun(4.7)-  0.6216169312],_
[4.8,  0.6142566003, stegun(4.8),  stegun(4.8)-  0.6142566003],_
[4.9,  0.6071468131, stegun(4.9),  stegun(4.9)-  0.6071468131],_
[5.0,  0.6002738587, stegun(5.0),  stegun(5.0)-  0.6002738587],_
[5.1,  0.5936250463, stegun(5.1),  stegun(5.1)-  0.5936250463],_
[5.2,  0.5871886062, stegun(5.2),  stegun(5.2)-  0.5871886062],_

[5.3,  0.5809536085, stegun(5.3),  stegun(5.3)-  0.5809536085],_
[5.4,  0.5749098871, stegun(5.4),  stegun(5.4)-  0.5749098871],_
[5.5,  0.5690479741, stegun(5.5),  stegun(5.5)-  0.5690479741],_
[5.6,  0.5633590393, stegun(5.6),  stegun(5.6)-  0.5633590393],_
[5.7,  0.5578348348, stegun(5.7),  stegun(5.7)-  0.5578348348],_
[5.8,  0.5524676495, stegun(5.8),  stegun(5.8)-  0.5524676495],_
[5.9,  0.5472502639, stegun(5.9),  stegun(5.9)-  0.5472502639],_
[6.0,  0.5421759104, stegun(6.0),  stegun(6.0)-  0.5421759104],_
[6.1,  0.5372382386, stegun(6.1),  stegun(6.1)-  0.5372382386],_
[6.2,  0.5324312833, stegun(6.2),  stegun(6.2)-  0.5324312833],_
[6.3,  0.5277494344, stegun(6.3),  stegun(6.3)-  0.5277494344],_
[6.4,  0.5231874101, stegun(6.4),  stegun(6.4)-  0.5231874101],_
[6.5,  0.5187402336, stegun(6.5),  stegun(6.5)-  0.5187402336],_
[6.6,  0.5144032108, stegun(6.6),  stegun(6.6)-  0.5144032108],_
[6.7,  0.5101719097, stegun(6.7),  stegun(6.7)-  0.5101719097],_
[6.8,  0.5060421421, stegun(6.8),  stegun(6.8)-  0.5060421421],_
[6.9,  0.5020099471, stegun(6.9),  stegun(6.9)-  0.5020099471],_
[7.0,  0.4980715749, stegun(7.0),  stegun(7.0)-  0.4980715749],_
[7.1,  0.4942234737, stegun(7.1),  stegun(7.1)-  0.4942234737],_
[7.2,  0.4904622755, stegun(7.2),  stegun(7.2)-  0.4904622755],_
[7.3,  0.4867847842, stegun(7.3),  stegun(7.3)-  0.4867847842],_
[7.4,  0.4831879648, stegun(7.4),  stegun(7.4)-  0.4831879648],_
[7.5,  0.4796689336, stegun(7.5),  stegun(7.5)-  0.4796689336],_
[7.6,  0.4762249486, stegun(7.6),  stegun(7.6)-  0.4762249486],_
[7.7,  0.4728533995, stegun(7.7),  stegun(7.7)-  0.4728533995],_
[7.8,  0.4695518010, stegun(7.8),  stegun(7.8)-  0.4695518010],_
[7.9,  0.4663177847, stegun(7.9),  stegun(7.9)-  0.4663177847],_
[8.0,  0.4631490928, stegun(8.0),  stegun(8.0)-  0.4631490928],_
[8.1,  0.4600435709, stegun(8.1),  stegun(8.1)-  0.4600435709],_
[8.2,  0.4569991615, stegun(8.2),  stegun(8.2)-  0.4569991615],_
[8.3,  0.4540139001, stegun(8.3),  stegun(8.3)-  0.4540139001],_
[8.4,  0.4510859089, stegun(8.4),  stegun(8.4)-  0.4510859089],_
[8.5,  0.4482133915, stegun(8.5),  stegun(8.5)-  0.4482133915],_
[8.6,  0.4453946295, stegun(8.6),  stegun(8.6)-  0.4453946295],_
[8.7,  0.4426279775, stegun(8.7),  stegun(8.7)-  0.4426279775],_
[8.8,  0.4399118594, stegun(8.8),  stegun(8.8)-  0.4399118594],_
[8.9,  0.4372447648, stegun(8.9),  stegun(8.9)-  0.4372447648],_
[9.0,  0.4346252454, stegun(9.0),  stegun(9.0)-  0.4346252454],_
[9.1,  0.4320519116, stegun(9.1),  stegun(9.1)-  0.4320519116],_
[9.2,  0.4295234301, stegun(9.2),  stegun(9.2)-  0.4295234301],_
[9.3,  0.4270385204, stegun(9.3),  stegun(9.3)-  0.4270385204],_
[9.4,  0.4245959520, stegun(9.4),  stegun(9.4)-  0.4245959520],_
[9.5,  0.4221945430, stegun(9.5),  stegun(9.5)-  0.4221945430],_
[9.6,  0.4198331565, stegun(9.6),  stegun(9.6)-  0.4198331565],_
[9.7,  0.4175106989, stegun(9.7),  stegun(9.7)-  0.4175106989],_
[9.8,  0.4152261179, stegun(9.8),  stegun(9.8)-  0.4152261179],_
[9.9,  0.4129784003, stegun(9.9),  stegun(9.9)-  0.4129784003],_
[10.0, 0.4107665704, stegun(10.0), stegun(10.0)- 0.4107665704]]
--E 6

)spool )lisp (bye) ———-

6

References

[1] Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp417-419