Values of Special Functions in format x,F(x) or x,y,F(x,y) Modified from 'Numerical Recipes' file FNCVAL.DAT: * Function values computed to 20 digits with Maple * Gamma values for negative arguments corrected * Some values modified or added ---------------------------------------------------------- Gamma Function 20 Values 1.0 1 1.2 0.91816874239976061064 1.4 0.88726381750307528922 1.6 0.89351534928769026144 1.8 0.93138377098024269891 2.0 1 0.2 4.5908437119988030532 0.4 2.2181595437576882231 0.6 1.4891922488128171024 0.8 1.1642297137253033736 -0.2 -5.8211485686265168682 -0.4 -3.7229806220320427560 -0.6 -3.6969325729294803718 -0.8 -5.7385546399985038165 10.0 362880 15.0 87178291200 20.0 121645100408832000 25.0 620448401733239439360000 30.0 8841761993739701954543616000000 34.0 8683317618811886495518194401280000000 N-factorial 20 Values 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3628800 11 39916800 12 479001600 13 6227020800 14 87178291200 15 1307674368000 17 355687428096000 20 2432902008176640000 25 15511210043330985984000000 30 265252859812191058636308480000000 33 8683317618811886495518194401280000000 Binomial Coefficients 20 Values 1 0 1 6 1 6 6 3 20 6 5 6 15 1 15 15 3 455 15 5 3003 15 7 6435 15 9 5005 15 11 1365 15 13 105 25 1 25 25 3 2300 25 5 53130 25 7 480700 25 9 2042975 25 11 4457400 25 13 5200300 25 15 3268760 25 17 1081575 Beta Function 15 Values 1.0 1.0 1 0.2 1.0 5 1.0 0.2 5 0.4 1.0 2.5 1.0 0.4 2.5 0.6 1.0 1.6666666666666666667 0.8 1.0 1.25 6.0 6.0 0.36075036075036075036E-3 6.0 5.0 0.79365079365079365079E-3 6.0 4.0 0.19841269841269841270E-2 6.0 3.0 0.59523809523809523810E-2 6.0 2.0 0.23809523809523809524E-1 7.0 7.0 0.83250083250083250083E-4 5.0 5.0 0.15873015873015873016E-2 4.0 4.0 0.71428571428571428571E-2 3.0 3.0 0.33333333333333333333E-1 2.0 2.0 0.16666666666666666667 Incomplete Gamma Function 20 Values 0.1 3.1622777E-02 0.74202633011827339557 0.1 3.1622777E-01 0.91197528812705340681 0.1 1.5811388 0.98989551656285465826 0.5 7.0710678E-02 0.29312793904634159044 0.5 7.0710678E-01 0.76564182421767055865 0.5 3.5355339 0.99216614455672814238 1.0 0.1000000 0.95162581964040426836E-1 1.0 1.0000000 0.63212055882855767840 1.0 5.0000000 0.99326205300091453290 1.1 1.0488088E-01 0.75747068686894339977E-1 1.1 1.0488088 0.60764566862795065345 1.1 5.2440442 0.99334248219419093387 2.0 1.4142136E-01 0.91053600382570441494E-2 2.0 1.4142136 0.41306429542590613092 2.0 7.0710678 0.99314503457159137928 6.0 2.4494897 0.38731816134312812698E-1 6.0 12.247449 0.98259366477918572616 11.0 16.583124 0.94042672794109771838 26.0 25.495098 0.48638661722196682228 41.0 44.821870 0.73597093301452448249 Error Function 20 Values 0.1 0.11246291601828489220 0.2 0.22270258921047845414 0.3 0.32862675945912742764 0.4 0.42839235504666845510 0.5 0.52049987781304653768 0.6 0.60385609084792592256 0.7 0.67780119383741847298 0.8 0.74210096470766048617 0.9 0.79690821242283212852 1.0 0.84270079294971486934 1.1 0.88020506957408169977 1.2 0.91031397822963538024 1.3 0.93400794494065243660 1.4 0.95228511976264881052 1.5 0.96610514647531072707 1.6 0.97634838334464400777 1.7 0.98379045859077456363 1.8 0.98909050163573071418 1.9 0.99279042923525746995 2.0 0.99532226501895273416 Incomplete Beta Function 20 Values 0.5 0.5 0.01 0.63768560858519847915E-1 0.5 0.5 0.10 0.20483276469913345164 0.5 0.5 1.00 1 1.0 0.5 0.01 0.50125628933800452655E-2 1.0 0.5 0.10 0.51316701949486200400E-1 1.0 0.5 1.00 1 1.0 1.0 0.5 0.5 5.0 5.0 0.5 0.5 10.0 0.5 0.9 0.15164090963470992063 10.0 5.0 0.5 0.89782714843750000000E-1 10.0 5.0 1.0 1 10.0 10.0 0.5 0.5 20.0 5.0 0.8 0.45987732975757912179 20.0 10.0 0.6 0.21468161023717389333 20.0 10.0 0.8 0.95073648269578749938 20.0 20.0 0.5 0.5 20.0 20.0 0.6 0.89794136871059179403 30.0 10.0 0.7 0.22412974918083661378 30.0 10.0 0.8 0.75864054871920859442 30.0 20.0 0.7 0.93001290669949261326 DiGamma Function 10 Values 0.01 -100.56088545786867450 0.1 -10.423754940411076795 0.5 -1.9635100260214234794 1 -0.57721566490153286061 1.5 0.36489973978576520559E-1 2 0.42278433509846713939 3 0.92278433509846713939 5 1.5061176684318004727 10 2.2517525890667211076 100 4.6001618527380874002 TriGamma Function 10 Values 0.01 10001.621213528313220 0.1 101.43329915079275882 0.5 4.9348022005446793094 1 1.6449340668482264365 1.5 0.93480220054467930942 2 0.64493406684822643647 3 0.39493406684822643647 5 0.22132295573711532536 10 0.10516633568168574612 100 0.10050166663333571395E-1