specfunc.dat

delphi矩阵运算、回归分析等数学计算

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