$SPAD/src/input exp.input

Timothy Daly December 3, 2016

Abstract

This compares Axiom’s exp function with the tables published in Abramowitz and Stegun.

Contents

2

In the following table there are 4 columns. The first column is the argument of exp(x), ranging from 0.0 to 10.0. The second column is the reference value of exp from the book Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp136-137

— * —

)set break resume
)spool exp.output
)set message test on
)set message auto off
)clear all
--S 1 of 2
[[0.0,     1.000000000000000,  exp(0.0), exp(0.0)-     1.000000000000000],_
[0.1,     1.105170918075648,  exp(0.1), exp(0.1)-     1.105170918075648],_
[0.2,     1.221402758160170,  exp(0.2), exp(0.2)-     1.221402758160170],_
[0.3,     1.349858807576003,  exp(0.3), exp(0.3)-     1.349858807576003],_
[0.4,     1.491824697641270,  exp(0.4), exp(0.4)-     1.491824697641270],_
[0.5,     1.648721270700128,  exp(0.5), exp(0.5)-     1.648721270700128],_
[0.6,     1.822118800390509,  exp(0.6), exp(0.6)-     1.822118800390509],_
[0.7,     2.013752707470477,  exp(0.7), exp(0.7)-     2.013752707470477],_
[0.8,     2.225540928492468,  exp(0.8), exp(0.8)-     2.225540928492468],_
[0.9,     2.459603111156950,  exp(0.9), exp(0.9)-     2.459603111156950],_
[1.0,     2.718281828459045,  exp(1.0), exp(1.0)-     2.718281828459045],_
[1.1,     3.004166023946433,  exp(1.1), exp(1.1)-     3.004166023946433],_
[1.2,     3.320116922736547,  exp(1.2), exp(1.2)-     3.320116922736547],_
[1.3,     3.669296667619244,  exp(1.3), exp(1.3)-     3.669296667619244],_
[1.4,     4.055199966844675,  exp(1.4), exp(1.4)-     4.055199966844675],_
[1.5,     4.481689070338065,  exp(1.5), exp(1.5)-     4.481689070338065],_
[1.6,     4.953032424395115,  exp(1.6), exp(1.6)-     4.953032424395115],_
[1.7,     5.473947391727200,  exp(1.7), exp(1.7)-     5.473947391727200],_
[1.8,     6.049647464412946,  exp(1.8), exp(1.8)-     6.049647464412946],_
[1.9,     6.685894442279269,  exp(1.9), exp(1.9)-     6.685894442279269],_
[2.0,     7.389056098930650,  exp(2.0), exp(2.0)-     7.389056098930650],_
[2.1,     8.166169912567650,  exp(2.1), exp(2.1)-     8.166169912567650],_
[2.2,     9.025013499434121,  exp(2.2), exp(2.2)-     9.025013499434121],_
[2.3,     9.974182454814721,  exp(2.3), exp(2.3)-     9.974182454814721],_
[2.4,    11.023176380641602,  exp(2.4), exp(2.4)-    11.023176380641602],_
[2.5,    12.182493960703473,  exp(2.5), exp(2.5)-    12.182493960703473],_
[2.6,    13.463738035001690,  exp(2.6), exp(2.6)-    13.463738035001690],_
[2.7,    14.879731724872834,  exp(2.7), exp(2.7)-    14.879731724872834],_
[2.8,    16.444646771097050,  exp(2.8), exp(2.8)-    16.444646771097050],_
[2.9,    18.174145369443061,  exp(2.9), exp(2.9)-    18.174145369443061],_
[3.0,    20.085536923187668,  exp(3.0), exp(3.0)-    20.085536923187668],_
[3.1,    22.197951281441633,  exp(3.1), exp(3.1)-    22.197951281441633],_
[3.2,    24.532530197109349,  exp(3.2), exp(3.2)-    24.532530197109349],_
[3.3,    27.112638920657887,  exp(3.3), exp(3.3)-    27.112638920657887],_
[3.4,    29.964100047397013,  exp(3.4), exp(3.4)-    29.964100047397013],_
[3.5,    33.115451958692314,  exp(3.5), exp(3.5)-    33.115451958692314],_

[3.6,    36.598234443677988,  exp(3.6), exp(3.6)-    36.598234443677988],_
[3.7,    40.447304360067391,  exp(3.7), exp(3.7)-    40.447304360067391],_
[3.8,    44.701184493300823,  exp(3.8), exp(3.8)-    44.701184493300823],_
[3.9,    49.402449105530174,  exp(3.9), exp(3.9)-    49.402449105530174],_
[4.0,    54.598150033144239,  exp(4.0), exp(4.0)-    54.598150033144239],_
[4.1,    60.340287597361969,  exp(4.1), exp(4.1)-    60.340287597361969],_
[4.2,    66.686331040925142,  exp(4.2), exp(4.2)-    66.686331040925142],_
[4.3,    73.699793699595797,  exp(4.3), exp(4.3)-    73.699793699595797],_
[4.4,    81.450868664968117,  exp(4.4), exp(4.4)-    81.450868664968117],_
[4.5,    90.017131300521814,  exp(4.5), exp(4.5)-    90.017131300521814],_
[4.6,    99.484315641933809,  exp(4.6), exp(4.6)-    99.484315641933809],_
[4.7,   109.947172452123499,  exp(4.7), exp(4.7)-   109.947172452123499],_
[4.8,   121.510417518734881,  exp(4.8), exp(4.8)-   121.510417518734881],_
[4.9,   134.289779684935485,  exp(4.9), exp(4.9)-   134.289779684935485],_
[5.0,   148.413159102577,     exp(5.0), exp(5.0)-   148.413159102577],_
[5.1,   164.021907299902,     exp(5.1), exp(5.1)-   164.021907299902],_
[5.2,   181.272241875151,     exp(5.2), exp(5.2)-   181.272241875151],_
[5.3,   200.336809974792,     exp(5.3), exp(5.3)-   200.336809974792],_
[5.4,   221.406416204187,     exp(5.4), exp(5.4)-   221.406416204187],_
[5.5,   244.691932264220,     exp(5.5), exp(5.5)-   244.691932264220],_
[5.6,   270.426407426153,     exp(5.6), exp(5.6)-   270.426407426153],_
[5.7,   298.867400967060,     exp(5.7), exp(5.7)-   298.867400967060],_
[5.8,   330.299559909649,     exp(5.8), exp(5.8)-   330.299559909649],_
[5.9,   365.037467865329,     exp(5.9), exp(5.9)-   365.037467865329],_
[6.0,   403.428793492735,     exp(6.0), exp(6.0)-   403.428793492735],_
[6.1,   445.857770082517,     exp(6.1), exp(6.1)-   445.857770082517],_
[6.2,   492.749041093256,     exp(6.2), exp(6.2)-   492.749041093256],_
[6.3,   544.571910125929,     exp(6.3), exp(6.3)-   544.571910125929],_
[6.4,   601.845037872082,     exp(6.4), exp(6.4)-   601.845037872082],_
[6.5,   665.141633044362,     exp(6.5), exp(6.5)-   665.141633044362],_
[6.6,   735.095189241973,     exp(6.6), exp(6.6)-   735.095189241973],_
[6.7,   812.405825167543,     exp(6.7), exp(6.7)-   812.405825167543],_
[6.8,   897.847291650418,     exp(6.8), exp(6.8)-   897.847291650418],_
[6.9,   992.274715605026,     exp(6.9), exp(6.9)-   992.274715605026],_
[7.0,  1096.633158428459,     exp(7.0), exp(7.0)-  1096.633158428459],_
[7.1,  1211.967074492577,     exp(7.1), exp(7.1)-  1211.967074492577],_
[7.2,  1339.430764394418,     exp(7.2), exp(7.2)-  1339.430764394418],_
[7.3,  1480.299927584545,     exp(7.3), exp(7.3)-  1480.299927584545],_
[7.4,  1635.984429995927,     exp(7.4), exp(7.4)-  1635.984429995927],_
[7.5,  1808.042414456063,     exp(7.5), exp(7.5)-  1808.042414456063],_
[7.6,  1998.195895104118,     exp(7.6), exp(7.6)-  1998.195895104118],_
[7.7,  2208.347991887209,     exp(7.7), exp(7.7)-  2208.347991887209],_
[7.8,  2440.601977624499,     exp(7.8), exp(7.8)-  2440.601977624499],_
[7.9,  2697.282328268509,     exp(7.9), exp(7.9)-  2697.282328268509],_
[8.0,  2980.957987041728,     exp(8.0), exp(8.0)-  2980.957987041728],_
[8.1,  3294.468075283841,     exp(8.1), exp(8.1)-  3294.468075283841],_
[8.2,  3640.950307332355,     exp(8.2), exp(8.2)-  3640.950307332355],_
[8.3,  4023.872393822310,     exp(8.3), exp(8.3)-  4023.872393822310],_
[8.4,  4447.066747699856,     exp(8.4), exp(8.4)-  4447.066747699856],_
[8.5,  4914.768840299134,     exp(8.5), exp(8.5)-  4914.768840299134],_

 [8.6,  5431.659591362980,     exp(8.6), exp(8.6)-  5431.659591362980],_
 [8.7,  6002.912217261022,     exp(8.7), exp(8.7)-  6002.912217261022],_
 [8.8,  6634.244006277885,     exp(8.8), exp(8.8)-  6634.244006277885],_
 [8.9,  7331.973539155993,     exp(8.9), exp(8.9)-  7331.973539155993],_
 [9.0,  8103.083927575384,     exp(9.0), exp(9.0)-  8103.083927575384],_
 [9.1,  8955.292703482512,     exp(9.1), exp(9.1)-  8955.292703482512],_
 [9.2,  9897.129058743916,     exp(9.2), exp(9.2)-  9897.129058743916],_
 [9.3, 10938.019208165184,     exp(9.3), exp(9.3)- 10938.019208165184],_
 [9.4, 12088.380730216984,     exp(9.4), exp(9.4)- 12088.380730216984],_
 [9.5, 13359.726829661872,     exp(9.5), exp(9.5)- 13359.726829661872],_
 [9.6, 14764.781565577273,     exp(9.6), exp(9.6)- 14764.781565577273],_
 [9.7, 16317.607198015432,     exp(9.7), exp(9.7)- 16317.607198015432],_
 [9.8, 18033.744927828511,     exp(9.8), exp(9.8)- 18033.744927828511],_
 [9.9, 19930.370438230289,     exp(9.9), exp(9.9)- 19930.370438230289],_
[10.0, 22026.465794806717,    exp(10.0), exp(10.0)-22026.465794806717]]
--R
--R
--R   (1)
--R   [[0.0,1.0,1.0,0.0],
--R    [0.1,1.1051709180 75648,1.1051709180 756476248,- 0.3752 E -15],
--R    [0.2,1.2214027581 6017,1.2214027581 601698339,- 0.1661 E -15],
--R    [0.3,1.3498588075 76003,1.3498588075 76003104,0.104 E -15],
--R    [0.4,1.4918246976 4127,1.4918246976 412703178,0.3178 E -15],
--R    [0.5,1.6487212707 00128,1.6487212707 001281468,0.1468 E -15],
--R    [0.6,1.8221188003 90509,1.8221188003 905089749,- 0.251 E -16],
--R    [0.7,2.0137527074 70477,2.0137527074 704765216,- 0.4784 E -15],
--R    [0.8,2.2255409284 92468,2.2255409284 924676046,- 0.3954 E -15],
--R    [0.9,2.4596031111 5695,2.4596031111 569496638,- 0.3362 E -15],
--R    [1.0,2.7182818284 59045,2.7182818284 590452354,0.2354 E -15],
--R    [1.1,3.0041660239 46433,3.0041660239 464331121,0.112 E -15],
--R    [1.2,3.3201169227 36547,3.3201169227 365474895,0.4895 E -15],
--R    [1.3,3.6692966676 19244,3.6692966676 192442204,0.22 E -15],
--R    [1.4,4.0551999668 44675,4.0551999668 446745872,- 0.413 E -15],
--R    [1.5,4.4816890703 38065,4.4816890703 380648226,- 0.177 E -15],
--R    [1.6,4.9530324243 95115,4.9530324243 951148037,- 0.196 E -15],
--R    [1.7,5.4739473917 272,5.4739473917 271997608,- 0.239 E -15],
--R    [1.8,6.0496474644 12946,6.0496474644 129460837,0.837 E -16],
--R    [1.9,6.6858944422 79269,6.6858944422 792694161,0.416 E -15],
--R    [2.0,7.3890560989 3065,7.3890560989 306502272,0.227 E -15],
--R    [2.1,8.1661699125 6765,8.1661699125 676500734,0.734 E -16],
--R    [2.2,9.0250134994 34121,9.0250134994 341209265,- 0.735 E -16],
--R    [2.3,9.9741824548 14721,9.9741824548 1472074,- 0.26 E -15],
--R    [2.4,11.0231763806 41602,11.0231763806 41601652,- 0.348 E -15],
--R    [2.5,12.1824939607 03473,12.1824939607 03473438,0.438 E -15],
--R    [2.6,13.4637380350 0169,13.4637380350 01690398,0.398 E -15],
--R    [2.7,14.8797317248 72834,14.8797317248 72834112,0.112 E -15],
--R    [2.8,16.4446467710 9705,16.4446467710 97049871,- 0.129 E -15],
--R    [2.9,18.1741453694 43061,18.1741453694 43060943,- 0.57 E -16],
--R    [3.0,20.0855369231 87668,20.0855369231 87667741,- 0.259 E -15],
--R    [3.1,22.1979512814 41633,22.1979512814 41633405,0.405 E -15],

--R    [3.2,24.5325301971 09349,24.5325301971 09348644,- 0.356 E -15],
--R    [3.3,27.1126389206 57887,27.1126389206 57887427,0.427 E -15],
--R    [3.4,29.9641000473 97013,29.9641000473 97013348,0.348 E -15],
--R    [3.5,33.1154519586 92314,33.1154519586 92313751,- 0.249 E -15],
--R    [3.6,36.5982344436 77988,36.5982344436 77987752,- 0.248 E -15],
--R    [3.7,40.4473043600 67391,40.4473043600 67390529,- 0.471 E -15],
--R    [3.8,44.7011844933 00823,44.7011844933 00823038,0.38 E -16],
--R    [3.9,49.4024491055 30174,49.4024491055 3017388,- 0.12 E -15],
--R    [4.0,54.5981500331 44239,54.5981500331 44239078,0.78 E -16],
--R    [4.1,60.3402875973 61969,60.3402875973 61969497,0.497 E -15],
--R    [4.2,66.6863310409 25142,66.6863310409 25141644,- 0.36 E -15],
--R    [4.3,73.6997936995 95797,73.6997936995 95796913,- 0.88 E -16],
--R    [4.4,81.4508686649 68117,81.4508686649 68117445,0.445 E -15],
--R    [4.5,90.0171313005 21814,90.0171313005 2181355,- 0.45 E -15],
--R    [4.6,99.4843156419 33809,99.4843156419 33808735,- 0.26 E -15],
--R    [4.7,109.9471724521 23499,109.9471724521 2349888,- 0.12 E -15],
--R    [4.8,121.5104175187 34881,121.5104175187 3488076,- 0.24 E -15],
--R    [4.9,134.2897796849 35485,134.2897796849 3548484,- 0.16 E -15],
--R    [5.0,148.4131591025 77,148.4131591025 7660342,- 0.39658 E -12],
--R    [5.1,164.0219072999 02,164.0219072999 0174394,- 0.25606 E -12],
--R    [5.2,181.2722418751 51,181.2722418751 5117937,0.17937 E -12],
--R    [5.3,200.3368099747 92,200.3368099747 9168484,- 0.31516 E -12],
--R    [5.4,221.4064162041 87,221.4064162041 8708703,0.8703 E -13],
--R    [5.5,244.6919322642 2,244.6919322642 2038792,0.38792 E -12],
--R    [5.6,270.4264074261 53,270.4264074261 5262815,- 0.37185 E -12],
--R    [5.7,298.8674009670 6,298.8674009670 6023267,0.23267 E -12],
--R    [5.8,330.2995599096 49,330.2995599096 4865412,- 0.34588 E -12],
--R    [5.9,365.0374678653 29,365.0374678653 2877732,- 0.2227 E -12],
--R    [6.0,403.4287934927 35,403.4287934927 3512261,0.1226 E -12],
--R    [6.1,445.8577700825 17,445.8577700825 1693179,- 0.6821 E -13],
--R    [6.2,492.7490410932 56,492.7490410932 5625456,0.25456 E -12],
--R    [6.3,544.5719101259 29,544.5719101259 2903306,0.331 E -13],
--R    [6.4,601.8450378720 82,601.8450378720 8205661,0.566 E -13],
--R    [6.5,665.1416330443 62,665.1416330443 6184069,- 0.1593 E -12],
--R    [6.6,735.0951892419 73,735.0951892419 728949,- 0.1051 E -12],
--R    [6.7,812.4058251675 43,812.4058251675 4311346,0.1135 E -12],
--R    [6.8,897.8472916504 18,897.8472916504 1769759,- 0.3024 E -12],
--R    [6.9,992.2747156050 26,992.2747156050 2587698,- 0.123 E -12],
--R    [7.0,1096.6331584284 59,1096.6331584284 585993,- 0.4007 E -12],
--R    [7.1,1211.9670744925 77,1211.9670744925 767212,- 0.2788 E -12],
--R    [7.2,1339.4307643944 18,1339.4307643944 178297,- 0.1703 E -12],
--R    [7.3,1480.2999275845 45,1480.2999275845 452229,0.2228 E -12],
--R    [7.4,1635.9844299959 27,1635.9844299959 265401,- 0.4599 E -12],
--R    [7.5,1808.0424144560 63,1808.0424144560 632069,0.2069 E -12],
--R    [7.6,1998.1958951041 18,1998.1958951041 179592,- 0.408 E -13],
--R    [7.7,2208.3479918872 09,2208.3479918872 08524,- 0.476 E -12],
--R    [7.8,2440.6019776244 99,2440.6019776244 990773,0.773 E -13],
--R    [7.9,2697.2823282685 09,2697.2823282685 088472,- 0.153 E -12],
--R    [8.0,2980.9579870417 28,2980.9579870417 282747,0.2747 E -12],
--R    [8.1,3294.4680752838 41,3294.4680752838 413332,0.3332 E -12],

--R    [8.2,3640.9503073323 55,3640.9503073323 547215,- 0.2785 E -12],
--R    [8.3,4023.8723938223 1,4023.8723938223 098416,- 0.158 E -12],
--R    [8.4,4447.0667476998 56,4447.0667476998 560855,0.855 E -13],
--R    [8.5,4914.7688402991 34,4914.7688402991 343754,0.375 E -12],
--R    [8.6,5431.6595913629 8,5431.6595913629 803217,0.322 E -12],
--R    [8.7,6002.9122172610 22,6002.9122172610 2198,- 0.2 E -13],
--R    [8.8,6634.2440062778 85,6634.2440062778 851586,0.159 E -12],
--R    [8.9,7331.9735391559 93,7331.9735391559 929051,- 0.949 E -13],
--R    [9.0,8103.0839275753 84,8103.0839275753 840077,0.77 E -14],
--R    [9.1,8955.2927034825 12,8955.2927034825 11711,- 0.289 E -12],
--R    [9.2,9897.1290587439 16,9897.1290587439 158867,- 0.113 E -12],
--R    [9.3,10938.0192081651 84,10938.0192081651 83753,- 0.247 E -12],
--R    [9.4,12088.3807302169 84,12088.3807302169 84397,0.397 E -12],
--R    [9.5,13359.7268296618 72,13359.7268296618 72276,0.276 E -12],
--R    [9.6,14764.7815655772 73,14764.7815655772 72616,- 0.384 E -12],
--R    [9.7,16317.6071980154 32,16317.6071980154 32233,0.233 E -12],
--R    [9.8,18033.7449278285 11,18033.7449278285 11246,0.246 E -12],
--R    [9.9,19930.3704382302 89,19930.3704382302 8949,0.49 E -12],
--R    [10.0,22026.4657948067 17,22026.4657948067 16517,- 0.483 E -12]]
--R                                                      Type: List(List(Float))
--E 1

———-

In the following table there are 4 columns. The first column is the argument of exp(-x), ranging from 0.0 to 10.0. The second column is the reference value of exp from the book Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp136-137

— * —

--S 2 of 2
[[0.1,0.90483741803595957316,exp(-0.1),exp(-0.1)-0.90483741803595957316],_
 [0.2,0.81873075307798185867,exp(-0.2),exp(-0.2)-0.81873075307798185867],_
 [0.3,0.74081822068171786607,exp(-0.3),exp(-0.3)-0.74081822068171786607],_
 [0.4,0.67032004603563930074,exp(-0.4),exp(-0.4)-0.67032004603563930074],_
 [0.5,0.60653065971263342360,exp(-0.5),exp(-0.5)-0.60653065971263342360],_
 [0.6,0.54881163609402643263,exp(-0.6),exp(-0.6)-0.54881163609402643263],_
 [0.7,0.49658530379140951470,exp(-0.7),exp(-0.7)-0.49658530379140951470],_
 [0.8,0.44932896411722159143,exp(-0.8),exp(-0.8)-0.44932896411722159143],_
 [0.9,0.40656965974059911188,exp(-0.9),exp(-0.9)-0.40656965974059911188],_
 [1.0,0.36787944117144232160,exp(-1.0),exp(-1.0)-0.36787944117144232160],_
 [1.1,0.33287108369807955329,exp(-1.1),exp(-1.1)-0.33287108369807955329],_
 [1.2,0.30119421191220209664,exp(-1.2),exp(-1.2)-0.30119421191220209664],_
 [1.3,0.27253179303401260312,exp(-1.3),exp(-1.3)-0.27253179303401260312],_
 [1.4,0.24659696394160647694,exp(-1.4),exp(-1.4)-0.24659696394160647694],_
 [1.5,0.22313016014842982893,exp(-1.5),exp(-1.5)-0.22313016014842982893],_
 [1.6,0.20189651799465540849,exp(-1.6),exp(-1.6)-0.20189651799465540849],_
 [1.7,0.18268352405273465022,exp(-1.7),exp(-1.7)-0.18268352405273465022],_
 [1.8,0.16529888822158653830,exp(-1.8),exp(-1.8)-0.16529888822158653830],_

[1.9,0.14956861922263505264,exp(-1.9),exp(-1.9)-0.14956861922263505264],_
[2.0,0.13533528323661269189,exp(-2.0),exp(-2.0)-0.13533528323661269189],_
[2.1,0.12245642825298191022,exp(-2.1),exp(-2.1)-0.12245642825298191022],_
[2.2,0.11080315836233388333,exp(-2.2),exp(-2.2)-0.11080315836233388333],_
[2.3,0.10025884372280373373,exp(-2.3),exp(-2.3)-0.10025884372280373373],_
[2.4,0.09071795328941250338,exp(-2.4),exp(-2.4)-0.09071795328941250338],_
[2.5,0.08208499862389879517,exp(-2.5),exp(-2.5)-0.08208499862389879517],_
[2.6,0.07427357821433388043,exp(-2.6),exp(-2.6)-0.07427357821433388043],_
[2.7,0.06720551273974976513,exp(-2.7),exp(-2.7)-0.06720551273974976513],_
[2.8,0.06081006262521796500,exp(-2.8),exp(-2.8)-0.06081006262521796500],_
[2.9,0.05502322005640722903,exp(-2.9),exp(-2.9)-0.05502322005640722903],_
[3.0,0.04978706836786394298,exp(-3.0),exp(-3.0)-0.04978706836786394298],_
[3.1,0.04504920239355780607,exp(-3.1),exp(-3.1)-0.04504920239355780607],_
[3.2,0.04076220397836621517,exp(-3.2),exp(-3.2)-0.04076220397836621517],_
[3.3,0.03688316740124000545,exp(-3.3),exp(-3.3)-0.03688316740124000545],_
[3.4,0.03337326996032607948,exp(-3.4),exp(-3.4)-0.03337326996032607948],_
[3.5,0.03019738342231850074,exp(-3.5),exp(-3.5)-0.03019738342231850074],_
[3.6,0.02732372244729256080,exp(-3.6),exp(-3.6)-0.02732372244729256080],_
[3.7,0.02472352647033939120,exp(-3.7),exp(-3.7)-0.02472352647033939120],_
[3.8,0.02237077185616559578,exp(-3.8),exp(-3.8)-0.02237077185616559578],_
[3.9,0.02024191144580438847,exp(-3.9),exp(-3.9)-0.02024191144580438847],_
[4.0,0.01831563888873418029,exp(-4.0),exp(-4.0)-0.01831563888873418029],_
[4.1,0.01657267540176124754,exp(-4.1),exp(-4.1)-0.01657267540176124754],_
[4.2,0.01499557682047770621,exp(-4.2),exp(-4.2)-0.01499557682047770621],_
[4.3,0.01356855901220093176,exp(-4.3),exp(-4.3)-0.01356855901220093176],_
[4.4,0.01227733990306844118,exp(-4.4),exp(-4.4)-0.01227733990306844118],_
[4.5,0.01110899653824230650,exp(-4.5),exp(-4.5)-0.01110899653824230650],_
[4.6,0.01005183574463358164,exp(-4.6),exp(-4.6)-0.01005183574463358164],_
[4.7,0.00909527710169581709,exp(-4.7),exp(-4.7)-0.00909527710169581709],_
[4.8,0.00822974704902002884,exp(-4.8),exp(-4.8)-0.00822974704902002884],_
[4.9,0.00744658307092434052,exp(-4.9),exp(-4.9)-0.00744658307092434052],_
[5.0,0.00673794699908546710,exp(-5.0),exp(-5.0)-0.00673794699908546710],_
[5.1,0.00609674656551563611,exp(-5.1),exp(-5.1)-0.00609674656551563611],_
[5.2,0.00551656442076077242,exp(-5.2),exp(-5.2)-0.00551656442076077242],_
[5.3,0.00499159390691021621,exp(-5.3),exp(-5.3)-0.00499159390691021621],_
[5.4,0.00451658094261266798,exp(-5.4),exp(-5.4)-0.00451658094261266798],_
[5.5,0.00408677143846406699,exp(-5.5),exp(-5.5)-0.00408677143846406699],_
[5.6,0.00369786371648293082,exp(-5.6),exp(-5.6)-0.00369786371648293082],_
[5.7,0.00334596545747127277,exp(-5.7),exp(-5.7)-0.00334596545747127277],_
[5.8,0.00302755474537581475,exp(-5.8),exp(-5.8)-0.00302755474537581475],_
[5.9,0.00273944481876836923,exp(-5.9),exp(-5.9)-0.00273944481876836923],_
[6.0,0.00247875217666635842,exp(-6.0),exp(-6.0)-0.00247875217666635842],_
[6.1,0.00224286771948580247,exp(-6.1),exp(-6.1)-0.00224286771948580247],_
[6.2,0.00202943063629573436,exp(-6.2),exp(-6.2)-0.00202943063629573436],_
[6.3,0.00183630477702890683,exp(-6.3),exp(-6.3)-0.00183630477702890683],_
[6.4,0.00166155727317393450,exp(-6.4),exp(-6.4)-0.00166155727317393450],_
[6.5,0.00150343919297757245,exp(-6.5),exp(-6.5)-0.00150343919297757245],_
[6.6,0.00136036803754789342,exp(-6.6),exp(-6.6)-0.00136036803754789342],_
[6.7,0.00123091190267348118,exp(-6.7),exp(-6.7)-0.00123091190267348118],_
[6.8,0.00111377514784480308,exp(-6.8),exp(-6.8)-0.00111377514784480308],_

[6.9,0.00100778542904851076,exp(-6.9),exp(-6.9)-0.00100778542904851076],_
[7.0,0.00091188196555451621,exp(-7.0),exp(-7.0)-0.00091188196555451621],_
[7.1,0.00082510492326590427,exp(-7.1),exp(-7.1)-0.00082510492326590427],_
[7.2,0.00074658580837667937,exp(-7.2),exp(-7.2)-0.00074658580837667937],_
[7.3,0.00067553877519384424,exp(-7.3),exp(-7.3)-0.00067553877519384424],_
[7.4,0.00061125276112957256,exp(-7.4),exp(-7.4)-0.00061125276112957256],_
[7.5,0.00055308437014783358,exp(-7.5),exp(-7.5)-0.00055308437014783358],_
[7.6,0.00050045143344061070,exp(-7.6),exp(-7.6)-0.00050045143344061070],_
[7.7,0.00045282718288679706,exp(-7.7),exp(-7.7)-0.00045282718288679706],_
[7.8,0.00040973497897978671,exp(-7.8),exp(-7.8)-0.00040973497897978671],_
[7.9,0.00037074354045908837,exp(-7.9),exp(-7.9)-0.00037074354045908837],_
[8.0,0.00033546262790251184,exp(-8.0),exp(-8.0)-0.00033546262790251184],_
[8.1,0.00030353913807886666,exp(-8.1),exp(-8.1)-0.00030353913807886666],_
[8.2,0.00027465356997214233,exp(-8.2),exp(-8.2)-0.00027465356997214233],_
[8.3,0.00024851682710795202,exp(-8.3),exp(-8.3)-0.00024851682710795202],_
[8.4,0.00022486732417884827,exp(-8.4),exp(-8.4)-0.00022486732417884827],_
[8.5,0.00020346836901064417,exp(-8.5),exp(-8.5)-0.00020346836901064417],_
[8.6,0.00018410579366757912,exp(-8.6),exp(-8.6)-0.00018410579366757912],_
[8.7,0.00016658581098763341,exp(-8.7),exp(-8.7)-0.00016658581098763341],_
[8.8,0.00015073307509547660,exp(-8.8),exp(-8.8)-0.00015073307509547660],_
[8.9,0.00013638892648201145,exp(-8.9),exp(-8.9)-0.00013638892648201145],_
[9.0,0.00012340980408667955,exp(-9.0),exp(-9.0)-0.00012340980408667955],_
[9.1,0.00011166580849011474,exp(-9.1),exp(-9.1)-0.00011166580849011474],_
[9.2,0.00010103940183709335,exp(-9.2),exp(-9.2)-0.00010103940183709335],_
[9.3,0.00009142423147817334,exp(-9.3),exp(-9.3)-0.00009142423147817334],_
[9.4,0.00008272406555663226,exp(-9.4),exp(-9.4)-0.00008272406555663226],_
[9.5,0.00007485182988770059,exp(-9.5),exp(-9.5)-0.00007485182988770059],_
[9.6,0.00006772873649085387,exp(-9.6),exp(-9.6)-0.00006772873649085387],_
[9.7,0.00006128349505322210,exp(-9.7),exp(-9.7)-0.00006128349505322210],_
[9.8,0.00005545159943217698,exp(-9.8),exp(-9.8)-0.00005545159943217698],_
[9.9,0.00005017468205617530,exp(-9.9),exp(-9.9)-0.00005017468205617530],_
[10.0,0.00004539992976248485,exp(-10.0),exp(-10.0)-0.00004539992976248485]]
--R
--R
--R   (2)
--R   [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20],
--R    [0.2,0.8187307530 7798185867,0.8187307530 7798185867,0.0],
--R    [0.3,0.7408182206 8171786607,0.7408182206 8171786606,- 0.7 E -20],
--R    [0.4,0.6703200460 3563930074,0.6703200460 3563930075,0.3 E -20],
--R    [0.5,0.6065306597 126334236,0.6065306597 126334236,0.3 E -20],
--R    [0.6,0.5488116360 9402643263,0.5488116360 9402643263,- 0.3 E -20],
--R    [0.7,0.4965853037 914095147,0.4965853037 9140951471,0.5 E -20],
--R    [0.8,0.4493289641 1722159143,0.4493289641 1722159143,0.0],
--R    [0.9,0.4065696597 4059911188,0.4065696597 4059911188,0.3 E -20],
--R    [1.0,0.3678794411 714423216,0.3678794411 7144232159,- 0.5 E -20],
--R    [1.1,0.3328710836 9807955329,0.3328710836 9807955329,- 0.2 E -20],
--R    [1.2,0.3011942119 1220209664,0.3011942119 1220209664,0.3 E -20],
--R    [1.3,0.2725317930 3401260312,0.2725317930 3401260312,0.3 E -20],
--R    [1.4,0.2465969639 4160647694,0.2465969639 4160647694,0.0],
--R    [1.5,0.2231301601 4842982893,0.2231301601 4842982893,0.3 E -20],

--R    [1.6,0.2018965179 9465540849,0.2018965179 9465540848,- 0.5 E -20],
--R    [1.7,0.1826835240 5273465022,0.1826835240 5273465022,0.3 E -20],
--R    [1.8,0.1652988882 215865383,0.1652988882 215865383,- 0.3 E -20],
--R    [1.9,0.1495686192 2263505264,0.1495686192 2263505264,0.8 E -21],
--R    [2.0,0.1353352832 3661269189,0.1353352832 3661269189,0.4 E -20],
--R    [2.1,0.1224564282 5298191022,0.1224564282 5298191022,- 0.8 E -21],
--R    [2.2,0.1108031583 6233388333,0.1108031583 6233388333,0.4 E -20],
--R    [2.3,0.1002588437 2280373373,0.1002588437 2280373373,0.0],
--R    [2.4,0.0907179532 8941250338,0.0907179532 8941250337 5,- 0.6 E -20],
--R    [2.5,0.0820849986 2389879517,0.0820849986 2389879516 9,- 0.4 E -21],
--R    [2.6,0.0742735782 1433388043,0.0742735782 1433388042 9,- 0.1 E -20],
--R    [2.7,0.0672055127 3974976513,0.0672055127 3974976512 6,- 0.4 E -20],
--R    [2.8,0.0608100626 25217965,0.0608100626 2521796499 6,- 0.4 E -20],
--R    [2.9,0.0550232200 5640722903,0.0550232200 5640722903,- 0.4 E -21],
--R    [3.0,0.0497870683 6786394298,0.0497870683 6786394297 9,- 0.6 E -21],
--R    [3.1,0.0450492023 9355780607,0.0450492023 9355780606 9,- 0.1 E -20],
--R    [3.2,0.0407622039 7836621517,0.0407622039 7836621516 6,- 0.4 E -20],
--R    [3.3,0.0368831674 0124000545,0.0368831674 0124000544 6,- 0.4 E -20],
--R    [3.4,0.0333732699 6032607948,0.0333732699 6032607948 2,0.2 E -20],
--R    [3.5,0.0301973834 2231850074,0.0301973834 2231850074,- 0.2 E -21],
--R    [3.6,0.0273237224 472925608,0.0273237224 4729256080 2,0.2 E -20],
--R    [3.7,0.0247235264 703393912,0.0247235264 7033939120 3,0.3 E -20],
--R    [3.8,0.0223707718 5616559578,0.0223707718 5616559577 9,- 0.1 E -20],
--R    [3.9,0.0202419114 4580438847,0.0202419114 4580438847 2,0.2 E -20],
--R    [4.0,0.0183156388 8873418029,0.0183156388 8873418029 4,0.4 E -20],
--R    [4.1,0.0165726754 0176124754,0.0165726754 0176124754 2,0.2 E -20],
--R    [4.2,0.0149955768 2047770621,0.0149955768 2047770621 2,0.2 E -20],
--R    [4.3,0.0135685590 1220093176,0.0135685590 1220093175 7,- 0.3 E -20],
--R    [4.4,0.0122773399 0306844118,0.0122773399 0306844117 9,- 0.1 E -20],
--R    [4.5,0.0111089965 382423065,0.0111089965 3824230649 6,- 0.4 E -20],
--R    [4.6,0.0100518357 4463358164,0.0100518357 4463358164 2,0.2 E -20],
--R    [4.7,0.0090952771 0169581709,0.0090952771 0169581709 21,0.2 E -20],
--R    [4.8,0.0082297470 4902002884,0.0082297470 4902002884 13,0.1 E -20],
--R    [4.9,0.0074465830 7092434052,0.0074465830 7092434051 82,- 0.2 E -20],
--R    [5.0,0.0067379469 990854671,0.0067379469 9908546709 66,- 0.3 E -20],
--R    [5.1,0.0060967465 6551563611,0.0060967465 6551563610 72,- 0.3 E -20],
--R    [5.2,0.0055165644 2076077242,0.0055165644 2076077241 81,- 0.2 E -20],
--R    [5.3,0.0049915939 0691021621,0.0049915939 0691021621 22,0.2 E -20],
--R    [5.4,0.0045165809 4261266798,0.0045165809 4261266798 16,0.2 E -20],
--R    [5.5,0.0040867714 3846406699,0.0040867714 3846406699 35,0.35 E -20],
--R    [5.6,0.0036978637 1648293082,0.0036978637 1648293082 07,0.7 E -21],
--R    [5.7,0.0033459654 5747127277,0.0033459654 5747127276 58,- 0.42 E -20],
--R    [5.8,0.0030275547 4537581475,0.0030275547 4537581474 82,- 0.18 E -20],
--R    [5.9,0.0027394448 1876836923,0.0027394448 1876836923 28,0.28 E -20],
--R    [6.0,0.0024787521 7666635842,0.0024787521 7666635842 3,0.3 E -20],
--R    [6.1,0.0022428677 1948580247,0.0022428677 1948580247 32,0.32 E -20],
--R    [6.2,0.0020294306 3629573436,0.0020294306 3629573436 34,0.34 E -20],
--R    [6.3,0.0018363047 7702890683,0.0018363047 7702890682 52,- 0.48 E -20],
--R    [6.4,0.0016615572 731739345,0.0016615572 7317393449 91,- 0.93 E -21],
--R    [6.5,0.0015034391 9297757245,0.0015034391 9297757244 74,- 0.26 E -20],

--R    [6.6,0.0013603680 3754789342,0.0013603680 3754789341 69,- 0.31 E -20],
--R    [6.7,0.0012309119 0267348118,0.0012309119 0267348118 46,0.46 E -20],
--R    [6.8,0.0011137751 4784480308,0.0011137751 4784480307 88,- 0.12 E -20],
--R    [6.9,0.0010077854 2904851076,0.0010077854 2904851076 14,0.14 E -20],
--R    [7.0,0.0009118819 6555451621,0.0009118819 6555451620 8,- 0.2 E -20],
--R    [7.1,0.0008251049 2326590427,0.0008251049 2326590427 015,0.1 E -21],
--R    [7.2,0.0007465858 0837667937,0.0007465858 0837667936 81,- 0.19 E -20],
--R    [7.3,0.0006755387 7519384424,0.0006755387 7519384423 783,- 0.22 E -20],
--R    [7.4,0.0006112527 6112957256,0.0006112527 6112957255 567,- 0.433 E -20],
--R    [7.5,0.0005530843 7014783358,0.0005530843 7014783358 31,0.31 E -20],
--R    [7.6,0.0005004514 334406107,0.0005004514 3344061069 551,- 0.449 E -20],
--R    [7.7,0.0004528271 8288679706,0.0004528271 8288679705 8,- 0.2 E -20],
--R    [7.8,0.0004097349 7897978671,0.0004097349 7897978670 846,- 0.15 E -20],
--R    [7.9,0.0003707435 4045908837,0.0003707435 4045908837 443,0.443 E -20],
--R    [8.0,0.0003354626 2790251184,0.0003354626 2790251183 882,- 0.12 E -20],
--R    [8.1,0.0003035391 3807886666,0.0003035391 3807886666 086,0.86 E -21],
--R    [8.2,0.0002746535 6997214233,0.0002746535 6997214232 763,- 0.237 E -20],
--R    [8.3,0.0002485168 2710795202,0.0002485168 2710795202 08,0.8 E -21],
--R    [8.4,0.0002248673 2417884827,0.0002248673 2417884827 28,0.28 E -20],
--R    [8.5,0.0002034683 6901064417,0.0002034683 6901064417 437,0.437 E -20],
--R    [8.6,0.0001841057 9366757912,0.0001841057 9366757912 495,0.495 E -20],
--R    [8.7,0.0001665858 1098763341,0.0001665858 1098763341 149,0.149 E -20],
--R    [8.8,0.0001507330 750954766,0.0001507330 7509547660 064,0.64 E -21],
--R    [8.9,0.0001363889 2648201145,0.0001363889 2648201144 785,- 0.215 E -20],
--R    [9.0,0.0001234098 0408667955,0.0001234098 0408667954 95,- 0.5 E -21],
--R    [9.1,0.0001116658 0849011474,0.0001116658 0849011473 564,- 0.436 E -20],
--R    [9.2,0.0001010394 0183709335,0.0001010394 0183709335 073,0.732 E -21],
--R    [9.3,0.0000914242 3147817334,0.0000914242 3147817333 7862,- 0.214 E -20],
--R    [9.4,0.0000827240 6555663226,0.0000827240 6555663226 2731,0.273 E -20],
--R    [9.5,0.0000748518 2988770059,0.0000748518 2988770059 1471,0.147 E -20],
--R    [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20],
--R    [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20],
--R    [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20],
--R    [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20],
--R    [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]]
--R                                                      Type: List(List(Float))
--E 2
)spool
)lisp (bye)

———-

References

[1] Abramowitz and Stegun, “Handbook of Mathematical Functions”, Dover Publications, Inc. New York 1965. pp136-137