Gamma function: Difference between revisions
→{{header|F Sharp}}
(→Lanczos: Conventional version.) |
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Line 1,354:
90 : 1.65079551625067E+136
100 : 9.33262154536104E+155
</pre>
{{Trans|C#}}
The C# version can be translated to F# to support complex numbers:
<syntaxhighlight lang="f sharp">
open System.Numerics
open System
let rec gamma (z: Complex) =
let mutable z = z
let lanczosCoefficients = [| 676.520368121885; -1259.1392167224; 771.323428777653; -176.615029162141; 12.5073432786869; -0.13857109526572; 9.98436957801957E-06; 1.50563273514931E-07 |]
if z.Real < 0.5 then
Math.PI / (sin (Math.PI * z) * gamma (1.0 - z))
else
let mutable x = Complex.One
z <- z - 1.0
for i = 0 to lanczosCoefficients.Length - 1 do
x <- x + lanczosCoefficients.[i] / (z + Complex(i, 0) + 1.0)
let t = z + float lanczosCoefficients.Length - 0.5
sqrt (2.0 * Math.PI) * (t ** (z + 0.5)) * exp (-t) * x
Seq.iter (fun i -> printfn "Gamma(%f) = %A" i (gamma (Complex(i, 0)))) [ 0 .. 100 ]
Seq.iter2 (fun i j -> printfn "Gamma(%f + i%f) = %A" i j (gamma (Complex(i, j)))) [ 0 .. 100 ] [ 0 .. 100 ]
</syntaxhighlight>
{{out}}
<pre>
Gamma(0.000000) = (NaN, NaN)
Gamma(1.000000) = (1,0000000000000049, 0)
Gamma(2.000000) = (1,0000000000000115, 0)
Gamma(3.000000) = (2,0000000000000386, 0)
Gamma(4.000000) = (6,000000000000169, 0)
Gamma(5.000000) = (24,00000000000084, 0)
Gamma(6.000000) = (120,00000000000514, 0)
Gamma(7.000000) = (720,0000000000364, 0)
Gamma(8.000000) = (5040,000000000289, 0)
Gamma(9.000000) = (40320,000000002554, 0)
Gamma(10.000000) = (362880,00000002526, 0)
Gamma(11.000000) = (3628800,0000002664, 0)
Gamma(12.000000) = (39916800,000003114, 0)
Gamma(13.000000) = (479001600,00004023, 0)
Gamma(14.000000) = (6227020800,000546, 0)
Gamma(15.000000) = (87178291200,00801, 0)
Gamma(16.000000) = (1307674368000,1267, 0)
Gamma(17.000000) = (20922789888002,08, 0)
Gamma(18.000000) = (355687428096034,7, 0)
Gamma(19.000000) = (6402373705728658, 0)
Gamma(20.000000) = (1,2164510040884514E+17, 0)
Gamma(21.000000) = (2,4329020081769083E+18, 0)
Gamma(22.000000) = (5,109094217171516E+19, 0)
Gamma(23.000000) = (1,1240007277777331E+21, 0)
Gamma(24.000000) = (2,5852016738887927E+22, 0)
Gamma(25.000000) = (6,20448401733312E+23, 0)
Gamma(26.000000) = (1,5511210043332811E+25, 0)
Gamma(27.000000) = (4,032914611266542E+26, 0)
Gamma(28.000000) = (1,0888869450419632E+28, 0)
Gamma(29.000000) = (3,048883446117507E+29, 0)
Gamma(30.000000) = (8,841761993740793E+30, 0)
Gamma(31.000000) = (2,652528598122235E+32, 0)
Gamma(32.000000) = (8,222838654178949E+33, 0)
Gamma(33.000000) = (2,631308369337265E+35, 0)
Gamma(34.000000) = (8,683317618812963E+36, 0)
Gamma(35.000000) = (2,9523279903964145E+38, 0)
Gamma(36.000000) = (1,0333147966387422E+40, 0)
Gamma(37.000000) = (3,719933267899472E+41, 0)
Gamma(38.000000) = (1,3763753091228064E+43, 0)
Gamma(39.000000) = (5,230226174666675E+44, 0)
Gamma(40.000000) = (2,0397882081200028E+46, 0)
Gamma(41.000000) = (8,159152832480012E+47, 0)
Gamma(42.000000) = (3,3452526613168034E+49, 0)
Gamma(43.000000) = (1,4050061177530564E+51, 0)
Gamma(44.000000) = (6,041526306338149E+52, 0)
Gamma(45.000000) = (2,658271574788788E+54, 0)
Gamma(46.000000) = (1,1962222086549537E+56, 0)
Gamma(47.000000) = (5,502622159812779E+57, 0)
Gamma(48.000000) = (2,586232415112008E+59, 0)
Gamma(49.000000) = (1,2413915592537631E+61, 0)
Gamma(50.000000) = (6,082818640343433E+62, 0)
Gamma(51.000000) = (3,04140932017172E+64, 0)
Gamma(52.000000) = (1,551118753287575E+66, 0)
Gamma(53.000000) = (8,065817517095389E+67, 0)
Gamma(54.000000) = (4,27488328406056E+69, 0)
Gamma(55.000000) = (2,308436973392699E+71, 0)
Gamma(56.000000) = (1,2696403353659833E+73, 0)
Gamma(57.000000) = (7,109985878049497E+74, 0)
Gamma(58.000000) = (4,0526919504882125E+76, 0)
Gamma(59.000000) = (2,350561331283167E+78, 0)
Gamma(60.000000) = (1,386831185457067E+80, 0)
Gamma(61.000000) = (8,3209871127424E+81, 0)
Gamma(62.000000) = (5,075802138772854E+83, 0)
Gamma(63.000000) = (3,1469973260391715E+85, 0)
Gamma(64.000000) = (1,9826083154046777E+87, 0)
Gamma(65.000000) = (1,2688693218589942E+89, 0)
Gamma(66.000000) = (8,247650592083449E+90, 0)
Gamma(67.000000) = (5,443449390775078E+92, 0)
Gamma(68.000000) = (3,647111091819299E+94, 0)
Gamma(69.000000) = (2,48003554243712E+96, 0)
Gamma(70.000000) = (1,711224524281613E+98, 0)
Gamma(71.000000) = (1,1978571669971308E+100, 0)
Gamma(72.000000) = (8,504785885679606E+101, 0)
Gamma(73.000000) = (6,123445837689312E+103, 0)
Gamma(74.000000) = (4,470115461513189E+105, 0)
Gamma(75.000000) = (3,307885441519755E+107, 0)
Gamma(76.000000) = (2,4809140811398187E+109, 0)
Gamma(77.000000) = (1,8854947016662648E+111, 0)
Gamma(78.000000) = (1,451830920283022E+113, 0)
Gamma(79.000000) = (1,1324281178207572E+115, 0)
Gamma(80.000000) = (8,946182130783977E+116, 0)
Gamma(81.000000) = (7,1569457046271725E+118, 0)
Gamma(82.000000) = (5,797126020748008E+120, 0)
Gamma(83.000000) = (4,753643337013366E+122, 0)
Gamma(84.000000) = (3,945523969721089E+124, 0)
Gamma(85.000000) = (3,31424013456571E+126, 0)
Gamma(86.000000) = (2,8171041143808564E+128, 0)
Gamma(87.000000) = (2,4227095383675335E+130, 0)
Gamma(88.000000) = (2,1077572983797526E+132, 0)
Gamma(89.000000) = (1,8548264225741817E+134, 0)
Gamma(90.000000) = (1,650795516091023E+136, 0)
Gamma(91.000000) = (1,4857159644819212E+138, 0)
Gamma(92.000000) = (1,3520015276785438E+140, 0)
Gamma(93.000000) = (1,2438414054642616E+142, 0)
Gamma(94.000000) = (1,1567725070817618E+144, 0)
Gamma(95.000000) = (1,0873661566568553E+146, 0)
Gamma(96.000000) = (1,032997848824012E+148, 0)
Gamma(97.000000) = (9,916779348710516E+149, 0)
Gamma(98.000000) = (9,619275968249195E+151, 0)
Gamma(99.000000) = (9,42689044888421E+153, 0)
Gamma(100.000000) = (9,33262154439535E+155, 0)
Gamma(0.000000 + i0.000000) = (NaN, NaN)
Gamma(1.000000 + i1.000000) = (0,49801566811835923, -0,15494982830180806)
Gamma(2.000000 + i2.000000) = (0,11229424234632254, 0,3236128855019324)
Gamma(3.000000 + i3.000000) = (-0,4401134076370088, -0,0636372431263299)
Gamma(4.000000 + i4.000000) = (0,7058649325913451, -0,49673908399741584)
Gamma(5.000000 + i5.000000) = (-0,9743952418053669, 2,0066898827226805)
Gamma(6.000000 + i6.000000) = (1,0560845455210948, -7,123931816061554)
Gamma(7.000000 + i7.000000) = (-0,26095668519941206, 27,88827411508434)
Gamma(8.000000 + i8.000000) = (1,8442848156317595, -125,96060801752867)
Gamma(9.000000 + i9.000000) = (-94,00399991734474, 643,3621714431141)
Gamma(10.000000 + i10.000000) = (1423,851941789479, -3496,081973308168)
Gamma(11.000000 + i11.000000) = (-16211,00700465313, 18168,810510285286)
Gamma(12.000000 + i12.000000) = (158471,8890918886, -68793,30331463458)
Gamma(13.000000 + i13.000000) = (-1329505,1052081874, -142199,12520863872)
Gamma(14.000000 + i14.000000) = (8576976,67312178, 7218722,503716219)
Gamma(15.000000 + i15.000000) = (-20768001,573587183, -99064686,32101583)
Gamma(16.000000 + i16.000000) = (-490395650,85195, 847486174,9207268)
Gamma(17.000000 + i17.000000) = (9782747798,66319, -2523864726,357996)
Gamma(18.000000 + i18.000000) = (-91408144092,80728, -62548333665,79536)
Gamma(19.000000 + i19.000000) = (80368797570,63837, 1283152922013,1064)
Gamma(20.000000 + i20.000000) = (12322153606702,379, -9813622771583,531)
Gamma(21.000000 + i21.000000) = (-191651224429571,5, -67416801166719,305)
Gamma(22.000000 + i22.000000) = (476610838765573,75, 2709614130691551,5)
Gamma(23.000000 + i23.000000) = (31282423285710508, -23340622982977492)
Gamma(24.000000 + i24.000000) = (-5,062346571412891E+17, -2,8075410996386413E+17)
Gamma(25.000000 + i25.000000) = (-1,1135374386470528E+18, 8,889271476011264E+18)
Gamma(26.000000 + i26.000000) = (1,4103207063357242E+20, -3,1111347801608966E+19)
Gamma(27.000000 + i27.000000) = (-1,20394153792971E+21, -2,100813378567903E+21)
Gamma(28.000000 + i28.000000) = (-2,9772583255514483E+22, 2,9845666640271078E+22)
Gamma(29.000000 + i29.000000) = (6,474322395366405E+23, 4,002110222682179E+23)
Gamma(30.000000 + i30.000000) = (4,982468347052982E+24, -1,3332730971666784E+25)
Gamma(31.000000 + i31.000000) = (-2,701233953257487E+26, -5,3335652308619844E+25)
Gamma(32.000000 + i32.000000) = (-3,5481927258667466E+26, 5,492417944693437E+27)
Gamma(33.000000 + i33.000000) = (1,13499763334942E+29, -3,936060260026878E+27)
Gamma(34.000000 + i34.000000) = (-2,497617380231244E+29, -2,4036706229026682E+30)
Gamma(35.000000 + i35.000000) = (-5,244047476964302E+31, 7,550247174479453E+30)
Gamma(36.000000 + i36.000000) = (1,8326953464053433E+32, 1,1815797667494789E+33)
Gamma(37.000000 + i37.000000) = (2,7496330950708185E+34, -3,7903032739968576E+33)
Gamma(38.000000 + i38.000000) = (-6,153702881069039E+34, -6,593476804299637E+35)
Gamma(39.000000 + i39.000000) = (-1,622188754583588E+37, 3,702408035066972E+35)
Gamma(40.000000 + i40.000000) = (-2,9787072201603815E+37, 4,069596487794187E+38)
Gamma(41.000000 + i41.000000) = (1,0327223226588694E+40, 2,028448840265614E+39)
Gamma(42.000000 + i42.000000) = (9,258591867044077E+40, -2,623834405446389E+41)
Gamma(43.000000 + i43.000000) = (-6,5825696143104E+42, -3,6674407207212435E+42)
Gamma(44.000000 + i44.000000) = (-1,3470021394042014E+44, 1,5970917674147318E+44)
Gamma(45.000000 + i45.000000) = (3,611191294816286E+45, 4,700641025433376E+45)
Gamma(46.000000 + i46.000000) = (1,572050028597055E+47, -6,978410499639601E+46)
Gamma(47.000000 + i47.000000) = (-8,064316457005957E+47, -5,037500759309252E+48)
Gamma(48.000000 + i48.000000) = (-1,5346852327090097E+50, -1,8750204416673013E+49)
Gamma(49.000000 + i49.000000) = (-1,963123049571723E+51, 4,3640542056764855E+51)
Gamma(50.000000 + i50.000000) = (1,112141672863102E+53, 1,0242389193853564E+53)
Gamma(51.000000 + i51.000000) = (4,3124175139534486E+54, -2,2723736598857867E+54)
Gamma(52.000000 + i52.000000) = (-1,9794169465380243E+55, -1,5907071359978385E+56)
Gamma(53.000000 + i53.000000) = (-5,198770735397539E+57, -1,364053254830618E+57)
Gamma(54.000000 + i54.000000) = (-1,120153853109903E+59, 1,4557034579325553E+59)
Gamma(55.000000 + i55.000000) = (3,0502206279504673E+60, 5,6213787579421754E+60)
Gamma(56.000000 + i56.000000) = (2,263901598439912E+62, -1,3869357395249425E+61)
Gamma(57.000000 + i57.000000) = (3,1337184675942048E+63, -7,566798379913671E+63)
Gamma(58.000000 + i58.000000) = (-1,9547779277051327E+65, -2,289059342042218E+65)
Gamma(59.000000 + i59.000000) = (-1,0990589957539216E+67, 2,43674092519427E+66)
Gamma(60.000000 + i60.000000) = (-1,2138821648921022E+68, 4,1070828497360523E+68)
Gamma(61.000000 + i61.000000) = (1,1429060333301634E+70, 1,199617402383565E+70)
Gamma(62.000000 + i62.000000) = (6,356301051435098E+71, -1,4385777048397157E+71)
Gamma(63.000000 + i63.000000) = (8,496122222382356E+72, -2,4629448359526944E+73)
Gamma(64.000000 + i64.000000) = (-6,555666234065589E+74, -8,308825832655404E+74)
Gamma(65.000000 + i65.000000) = (-4,35298630131942E+76, 3,566503620394996E+75)
Gamma(66.000000 + i66.000000) = (-9,093720755985274E+77, 1,5886817012950856E+78)
Gamma(67.000000 + i67.000000) = (3,276704637172729E+79, 7,067540192000104E+79)
Gamma(68.000000 + i68.000000) = (3,3000031716552424E+81, 6,606403155114497E+80)
Gamma(69.000000 + i69.000000) = (1,1027558271573558E+83, -9,8053446601259E+82)
Gamma(70.000000 + i70.000000) = (-4,322638823338879E+83, -6,551055369074648E+84)
Gamma(71.000000 + i71.000000) = (-2,4300476213174805E+86, -1,695901195606269E+86)
Gamma(72.000000 + i72.000000) = (-1,3066738432408389E+88, 3,647419995967721E+87)
Gamma(73.000000 + i73.000000) = (-2,631035116210543E+89, 5,722329713478048E+89)
Gamma(74.000000 + i74.000000) = (1,2168690154152985E+91, 2,7033309001464033E+91)
Gamma(75.000000 + i75.000000) = (1,3482397421660745E+93, 4,28037329878204E+92)
Gamma(76.000000 + i76.000000) = (5,937687180258459E+94, -3,3970662984923895E+94)
Gamma(77.000000 + i77.000000) = (7,877518886977203E+95, -3,258429077036584E+96)
Gamma(78.000000 + i78.000000) = (-8,893580405683355E+97, -1,4068641589865653E+98)
Gamma(79.000000 + i79.000000) = (-8,171120040126758E+99, -1,8182361788970335E+99)
Gamma(80.000000 + i80.000000) = (-3,620672062418723E+101, 2,252383956928435E+101)
Gamma(81.000000 + i81.000000) = (-5,470323981863164E+102, 2,130475015794634E+103)
Gamma(82.000000 + i82.000000) = (5,5003853678128614E+104, 1,0085770500872239E+105)
Gamma(83.000000 + i83.000000) = (5,740274728712029E+106, 1,986132310865518E+106)
Gamma(84.000000 + i84.000000) = (3,002634263016605E+108, -1,245707037705857E+108)
Gamma(85.000000 + i85.000000) = (7,865153067057636E+109, -1,575289481058232E+110)
Gamma(86.000000 + i86.000000) = (-2,2903303039804873E+111, -9,374401780068583E+111)
Gamma(87.000000 + i87.000000) = (-4,291880277570836E+113, -3,196185984412844E+113)
Gamma(88.000000 + i88.000000) = (-2,9995707183640408E+115, 1,1845722184191957E+114)
Gamma(89.000000 + i89.000000) = (-1,2943245318203042E+117, 1,1073023439932073E+117)
Gamma(90.000000 + i90.000000) = (-2,0007723042777158E+118, 9,568042990491017E+118)
Gamma(91.000000 + i91.000000) = (2,4147687416625443E+120, 5,132960890087842E+120)
Gamma(92.000000 + i92.000000) = (2,9270673985442265E+122, 1,5846423875074053E+122)
Gamma(93.000000 + i93.000000) = (1,9583971561168918E+124, -2,5166936071920716E+123)
Gamma(94.000000 + i94.000000) = (8,735240498823332E+125, -7,993043748530299E+125)
Gamma(95.000000 + i95.000000) = (1,6159775690644545E+127, -6,9922194609237035E+127)
Gamma(96.000000 + i96.000000) = (-1,569012926564151E+129, -4,10649302643008E+129)
Gamma(97.000000 + i97.000000) = (-2,2080981691082815E+131, -1,5902953016632018E+131)
Gamma(98.000000 + i98.000000) = (-1,6995881449793942E+133, -8,982249136857376E+131)
Gamma(99.000000 + i99.000000) = (-9,394719018633069E+134, 5,234766160326565E+134)
Gamma(100.000000 + i100.000000) = (-3,3597454530316526E+136, 5,986962556433683E+136)
</pre>
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