69 lines
6.0 KiB
Rexx
69 lines
6.0 KiB
Rexx
/*REXX program calculates GAMMA using the Taylor series coefficients; ≈80 decimal digits*/
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/*The GAMMA function symbol is the Greek capital letter: Γ */
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numeric digits 90 /*be able to handle extended precision.*/
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parse arg LO HI . /*allow specification of gamma arg/args*/
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/* [↓] either show a range or a ··· */
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do j=word(LO 1, 1) to word(HI LO 9, 1) /* ··· single gamma value.*/
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say 'gamma('j") =" gamma(j) /*compute gamma of J and display value.*/
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end /*j*/ /* [↑] default LO is one; HI is nine.*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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gamma: procedure; parse arg x; xm=x-1; sum=0
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/*coefficients thanks to: Arne Fransén & Staffan Wrigge.*/
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#.1 = 1 /* [↓] #.2 is the Euler-Mascheroni constant. */
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#.2 = 0.57721566490153286060651209008240243104215933593992359880576723488486772677766467
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#.3 = -0.65587807152025388107701951514539048127976638047858434729236244568387083835372210
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#.4 = -0.04200263503409523552900393487542981871139450040110609352206581297618009687597599
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#.5 = 0.16653861138229148950170079510210523571778150224717434057046890317899386605647425
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#.6 = -0.04219773455554433674820830128918739130165268418982248637691887327545901118558900
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#.7 = -0.00962197152787697356211492167234819897536294225211300210513886262731167351446074
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#.8 = 0.00721894324666309954239501034044657270990480088023831800109478117362259497415854
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#.9 = -0.00116516759185906511211397108401838866680933379538405744340750527562002584816653
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#.10 = -0.00021524167411495097281572996305364780647824192337833875035026748908563946371678
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#.11 = 0.00012805028238811618615319862632816432339489209969367721490054583804120355204347
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#.12 = -0.00002013485478078823865568939142102181838229483329797911526116267090822918618897
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#.13 = -0.00000125049348214267065734535947383309224232265562115395981534992315749121245561
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#.14 = 0.00000113302723198169588237412962033074494332400483862107565429550539546040842730
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#.15 = -0.00000020563384169776071034501541300205728365125790262933794534683172533245680371
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#.16 = 0.00000000611609510448141581786249868285534286727586571971232086732402927723507435
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#.17 = 0.00000000500200764446922293005566504805999130304461274249448171895337887737472132
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#.18 = -0.00000000118127457048702014458812656543650557773875950493258759096189263169643391
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#.19 = 0.00000000010434267116911005104915403323122501914007098231258121210871073927347588
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#.20 = 0.00000000000778226343990507125404993731136077722606808618139293881943550732692987
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#.21 = -0.00000000000369680561864220570818781587808576623657096345136099513648454655443000
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#.22 = 0.00000000000051003702874544759790154813228632318027268860697076321173501048565735
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#.23 = -0.00000000000002058326053566506783222429544855237419746091080810147188058196444349
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#.24 = -0.00000000000000534812253942301798237001731872793994898971547812068211168095493211
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#.25 = 0.00000000000000122677862823826079015889384662242242816545575045632136601135999606
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#.26 = -0.00000000000000011812593016974587695137645868422978312115572918048478798375081233
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#.27 = 0.00000000000000000118669225475160033257977724292867407108849407966482711074006109
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#.28 = 0.00000000000000000141238065531803178155580394756670903708635075033452562564122263
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#.29 = -0.00000000000000000022987456844353702065924785806336992602845059314190367014889830
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#.30 = 0.00000000000000000001714406321927337433383963370267257066812656062517433174649858
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#.31 = 0.00000000000000000000013373517304936931148647813951222680228750594717618947898583
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#.32 = -0.00000000000000000000020542335517666727893250253513557337960820379352387364127301
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#.33 = 0.00000000000000000000002736030048607999844831509904330982014865311695836363370165
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#.34 = -0.00000000000000000000000173235644591051663905742845156477979906974910879499841377
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#.35 = -0.00000000000000000000000002360619024499287287343450735427531007926413552145370486
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#.36 = 0.00000000000000000000000001864982941717294430718413161878666898945868429073668232
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#.37 = -0.00000000000000000000000000221809562420719720439971691362686037973177950067567580
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#.38 = 0.00000000000000000000000000012977819749479936688244144863305941656194998646391332
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#.39 = 0.00000000000000000000000000000118069747496652840622274541550997151855968463784158
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#.40 = -0.00000000000000000000000000000112458434927708809029365467426143951211941179558301
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#.41 = 0.00000000000000000000000000000012770851751408662039902066777511246477487720656005
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#.42 = -0.00000000000000000000000000000000739145116961514082346128933010855282371056899245
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#.43 = 0.00000000000000000000000000000000001134750257554215760954165259469306393008612196
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#.44 = 0.00000000000000000000000000000000004639134641058722029944804907952228463057968680
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#.45 = -0.00000000000000000000000000000000000534733681843919887507741819670989332090488591
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#.46 = 0.00000000000000000000000000000000000032079959236133526228612372790827943910901464
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#.47 = -0.00000000000000000000000000000000000000444582973655075688210159035212464363740144
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#.48 = -0.00000000000000000000000000000000000000131117451888198871290105849438992219023663
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#.49 = 0.00000000000000000000000000000000000000016470333525438138868182593279063941453996
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#.50 = -0.00000000000000000000000000000000000000001056233178503581218600561071538285049997
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#.51 = 0.00000000000000000000000000000000000000000026784429826430494783549630718908519485
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#.52 = 0.00000000000000000000000000000000000000000002424715494851782689673032938370921241
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#=52; do k=# by -1 for #
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sum=sum*xm + #.k
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end /*k*/
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return 1/sum
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