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- Values of Special Functions in format x,F(x) or x,y,F(x,y)
- Gamma Function
- 17 Values
- 1.0 1.000000
- 1.2 0.918169
- 1.4 0.887264
- 1.6 0.893515
- 1.8 0.931384
- 2.0 1.000000
- 0.2 4.590845
- 0.4 2.218160
- 0.6 1.489192
- 0.8 1.164230
- -0.2 5.2005665E01
- -0.4 4.617091E01
- -0.6 4.0128959E01
- -0.8 3.4231564E01
- 10.0 3.6288000E05
- 20.0 1.2164510E17
- 30.0 8.8417620E30
- N-factorial
- 18 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 1.3076755E12
- 20 2.4329042E18
- 25 1.5511222E25
- 30 2.6525281E32
- 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 1.000000
- 0.2 1.0 5.000000
- 1.0 0.2 5.000000
- 0.4 1.0 2.500000
- 1.0 0.4 2.500000
- 0.6 1.0 1.666667
- 0.8 1.0 1.250000
- 6.0 6.0 3.607504E-04
- 6.0 5.0 7.936508E-04
- 6.0 4.0 1.984127E-03
- 6.0 3.0 5.952381E-03
- 6.0 2.0 0.238095E-01
- 7.0 7.0 8.325008E-05
- 5.0 5.0 1.587302E-03
- 4.0 4.0 7.142857E-03
- 3.0 3.0 0.333333E-01
- 2.0 2.0 1.666667E-01
- Incomplete Gamma Function
- 20 Values
- 0.1 3.1622777E-02 0.7420263
- 0.1 3.1622777E-01 0.9119753
- 0.1 1.5811388 0.9898955
- 0.5 7.0710678E-02 0.2931279
- 0.5 7.0710678E-01 0.7656418
- 0.5 3.5355339 0.9921661
- 1.0 0.1000000 0.0951626
- 1.0 1.0000000 0.6321206
- 1.0 5.0000000 0.9932621
- 1.1 1.0488088E-01 0.0757471
- 1.1 1.0488088 0.6076457
- 1.1 5.2440442 0.9933425
- 2.0 1.4142136E-01 0.0091054
- 2.0 1.4142136 0.4130643
- 2.0 7.0710678 0.9931450
- 6.0 2.4494897 0.0387318
- 6.0 12.247449 0.9825937
- 11.0 16.583124 0.9404267
- 26.0 25.495098 0.4863866
- 41.0 44.821870 0.7359709
- Error Function
- 20 Values
- 0.0 0.000000
- 0.1 0.1124629
- 0.2 0.2227026
- 0.3 0.3286268
- 0.4 0.4283924
- 0.5 0.5204999
- 0.6 0.6038561
- 0.7 0.6778012
- 0.8 0.7421010
- 0.9 0.7969082
- 1.0 0.8427008
- 1.1 0.8802051
- 1.2 0.9103140
- 1.3 0.9340079
- 1.4 0.9522851
- 1.5 0.9661051
- 1.6 0.9763484
- 1.7 0.9837905
- 1.8 0.9890905
- 1.9 0.9927904
- Incomplete Beta Function
- 20 Values
- 0.5 0.5 0.01 0.0637686
- 0.5 0.5 0.10 0.2048328
- 0.5 0.5 1.00 1.0000000
- 1.0 0.5 0.01 0.0050126
- 1.0 0.5 0.10 0.0513167
- 1.0 0.5 1.00 1.0000000
- 1.0 1.0 0.5 0.5000000
- 5.0 5.0 0.5 0.5000000
- 10.0 0.5 0.9 0.1516409
- 10.0 5.0 0.5 0.0897827
- 10.0 5.0 1.0 1.0000000
- 10.0 10.0 0.5 0.5000000
- 20.0 5.0 0.8 0.4598773
- 20.0 10.0 0.6 0.2146816
- 20.0 10.0 0.8 0.9507365
- 20.0 20.0 0.5 0.5000000
- 20.0 20.0 0.6 0.8979414
- 30.0 10.0 0.7 0.2241297
- 30.0 10.0 0.8 0.7586405
- 40.0 20.0 0.7 0.7001783
- Bessel Function J0
- 20 Values
- -5.0 -0.1775968
- -4.0 -0.3971498
- -3.0 -0.2600520
- -2.0 0.2238908
- -1.0 0.7651976
- 0.0 1.0000000
- 1.0 0.7651977
- 2.0 0.2238908
- 3.0 -0.2600520
- 4.0 -0.3971498
- 5.0 -0.1775968
- 6.0 0.1506453
- 7.0 0.3000793
- 8.0 0.1716508
- 9.0 -0.0903336
- 10.0 -0.2459358
- 11.0 -0.1711903
- 12.0 0.0476893
- 13.0 0.2069261
- 14.0 0.1710735
- 15.0 -0.0142245
- Bessel Function Y0
- 15 Values
- 0.1 -1.5342387
- 1.0 0.0882570
- 2.0 0.51037567
- 3.0 0.37685001
- 4.0 -0.0169407
- 5.0 -0.3085176
- 6.0 -0.2881947
- 7.0 -0.0259497
- 8.0 0.2235215
- 9.0 0.2499367
- 10.0 0.0556712
- 11.0 -0.1688473
- 12.0 -0.2252373
- 13.0 -0.0782079
- 14.0 0.1271926
- 15.0 0.2054743
- Bessel Function J1
- 20 Values
- -5.0 0.3275791
- -4.0 0.0660433
- -3.0 -0.3390590
- -2.0 -0.5767248
- -1.0 -0.4400506
- 0.0 0.0000000
- 1.0 0.4400506
- 2.0 0.5767248
- 3.0 0.3390590
- 4.0 -0.0660433
- 5.0 -0.3275791
- 6.0 -0.2766839
- 7.0 -0.0046828
- 8.0 0.2346364
- 9.0 0.2453118
- 10.0 0.0434728
- 11.0 -0.1767853
- 12.0 -0.2234471
- 13.0 -0.0703181
- 14.0 0.1333752
- 15.0 0.2051040
- Bessel Function Y1
- 15 Values
- 0.1 -6.4589511
- 1.0 -0.7812128
- 2.0 -0.1070324
- 3.0 0.3246744
- 4.0 0.3979257
- 5.0 0.1478631
- 6.0 -0.1750103
- 7.0 -0.3026672
- 8.0 -0.1580605
- 9.0 0.1043146
- 10.0 0.2490154
- 11.0 0.1637055
- 12.0 -0.0570992
- 13.0 -0.2100814
- 14.0 -0.1666448
- 15.0 0.0210736
- Bessel Function Jn, n>=2
- 20 Values
- 2 1.0 1.149034849E-01
- 2 2.0 3.528340286E-01
- 2 5.0 4.656511628E-02
- 2 10.0 2.546303137E-01
- 2 50.0 -5.971280079E-02
- 5 1.0 2.497577302E-04
- 5 2.0 7.039629756E-03
- 5 5.0 2.611405461E-01
- 5 10.0 -2.340615282E-01
- 5 50.0 -8.140024770E-02
- 10 1.0 2.630615124E-10
- 10 2.0 2.515386283E-07
- 10 5.0 1.467802647E-03
- 10 10.0 2.074861066E-01
- 10 50.0 -1.138478491E-01
- 20 1.0 3.873503009E-25
- 20 2.0 3.918972805E-19
- 20 5.0 2.770330052E-11
- 20 10.0 1.151336925E-05
- 20 50.0 -1.167043528E-01
- Bessel Function Yn, n>=2
- 20 Values
- 2 1.0 -1.650682607
- 2 2.0 -6.174081042E-01
- 2 5.0 3.676628826E-01
- 2 10.0 -5.868082460E-03
- 2 50.0 9.579316873E-02
- 5 1.0 -2.604058666E02
- 5 2.0 -9.935989128
- 5 5.0 -4.536948225E-01
- 5 10.0 1.354030477E-01
- 5 50.0 -7.854841391E-02
- 10 1.0 -1.216180143E08
- 10 2.0 -1.291845422E05
- 10 5.0 -2.512911010E01
- 10 10.0 -3.598141522E-01
- 10 50.0 5.723897182E-03
- 20 1.0 -4.113970315E22
- 20 2.0 -4.081651389E16
- 20 5.0 -5.933965297E08
- 20 10.0 -1.597483848E03
- 20 50.0 1.644263395E-02
- Modified Bessel Function I0
- 20 Values
- 0.0 1.0000000
- 0.2 1.0100250
- 0.4 1.0404018
- 0.6 1.0920453
- 0.8 1.1665149
- 1.0 1.2660658
- 1.2 1.3937256
- 1.4 1.5533951
- 1.6 1.7499807
- 1.8 1.9895593
- 2.0 2.2795852
- 2.5 3.2898391
- 3.0 4.8807925
- 3.5 7.3782035
- 4.0 11.301922
- 4.5 17.481172
- 5.0 27.239871
- 6.0 67.234406
- 8.0 427.56411
- 10.0 2815.7167
- Modified Bessel Function K0
- 20 Values
- 0.1 2.4270690
- 0.2 1.7527038
- 0.4 1.1145291
- 0.6 0.77752208
- 0.8 0.56534710
- 1.0 0.42102445
- 1.2 0.31850821
- 1.4 0.24365506
- 1.6 0.18795475
- 1.8 0.14593140
- 2.0 0.11389387
- 2.5 6.2347553E-02
- 3.0 3.4739500E-02
- 3.5 1.9598897E-02
- 4.0 1.1159676E-02
- 4.5 6.3998572E-03
- 5.0 3.6910983E-03
- 6.0 1.2439943E-03
- 8.0 1.4647071E-04
- 10.0 1.7780062E-05
- Modified Bessel Function I1
- 20 Values
- 0.0 0.00000000
- 0.2 0.10050083
- 0.4 0.20402675
- 0.6 0.31370403
- 0.8 0.43286480
- 1.0 0.56515912
- 1.2 0.71467794
- 1.4 0.88609197
- 1.6 1.0848107
- 1.8 1.3171674
- 2.0 1.5906369
- 2.5 2.5167163
- 3.0 3.9533700
- 3.5 6.2058350
- 4.0 9.7594652
- 4.5 15.389221
- 5.0 24.335643
- 6.0 61.341937
- 8.0 399.87313
- 10.0 2670.9883
- Modified Bessel Function K1
- 20 Values
- 0.1 9.8538451
- 0.2 4.7759725
- 0.4 2.1843544
- 0.6 1.3028349
- 0.8 0.86178163
- 1.0 0.60190724
- 1.2 0.43459241
- 1.4 0.32083589
- 1.6 0.24063392
- 1.8 0.18262309
- 2.0 0.13986588
- 2.5 7.3890816E-02
- 3.0 4.0156431E-02
- 3.5 2.2239393E-02
- 4.0 1.2483499E-02
- 4.5 7.0780949E-03
- 5.0 4.0446134E-03
- 6.0 1.3439197E-03
- 8.0 1.5536921E-04
- 10.0 1.8648773E-05
- Modified Bessel Function Kn, n>=2
- 28 Values
- 2 0.2 49.512430
- 2 1.0 1.6248389
- 2 2.0 2.5375975E-01
- 2 2.5 1.2146021E-01
- 2 3.0 6.1510459E-02
- 2 5.0 5.3089437E-03
- 2 10.0 2.1509817E-05
- 2 20.0 6.3295437E-10
- 3 1.0 7.101262825
- 3 2.0 6.473853909E-01
- 3 5.0 8.291768415E-03
- 3 10.0 2.725270026E-05
- 3 50.0 3.72793677E-23
- 5 1.0 3.609605896E02
- 5 2.0 9.431049101
- 5 5.0 3.270627371E-02
- 5 10.0 5.754184999E-05
- 5 50.0 4.36718224E-23
- 10 1.0 1.807132899E08
- 10 2.0 1.624824040E05
- 10 5.0 9.758562829
- 10 10.0 1.614255300E-03
- 10 50.0 9.15098819E-23
- 20 1.0 6.294369369E22
- 20 2.0 5.770856853E16
- 20 5.0 4.827000521E08
- 20 10.0 1.787442782E02
- 20 50.0 1.70614838E-21
- Modified Bessel Function In, n>=2
- 28 Values
- 2 0.2 5.0166876E-03
- 2 1.0 1.3574767E-01
- 2 2.0 6.8894844E-01
- 2 2.5 1.2764661
- 2 3.0 2.2452125
- 2 5.0 17.505615
- 2 10.0 2281.5189
- 2 20.0 3.9312785E07
- 3 1.0 2.216842492E-02
- 3 2.0 2.127399592E-01
- 3 5.0 1.033115017E01
- 3 10.0 1.758380717E01
- 3 50.0 2.67776414E20
- 5 1.0 2.714631560E-04
- 5 2.0 9.825679323E-03
- 5 5.0 2.157974547
- 5 10.0 7.771882864E02
- 5 50.0 2.27854831E20
- 10 1.0 2.752948040E-10
- 10 2.0 3.016963879E-07
- 10 5.0 4.580044419E-03
- 10 10.0 2.189170616E01
- 10 50.0 1.07159716E20
- 20 1.0 3.966835986E-25
- 20 2.0 4.310560576E-19
- 20 5.0 5.024239358E-11
- 20 10.0 1.250799736E-04
- 20 50.0 5.44200840E18
- Legendre Polynomials
- 19 Values
- 1 0 1.0 1.224745
- 10 0 1.0 3.240370
- 20 0 1.0 4.527693
- 1 0 0.7071067 0.866025
- 10 0 0.7071067 0.373006
- 20 0 0.7071067 -0.874140
- 1 0 0.0 0.000000
- 10 0 0.0 -0.797435
- 20 0 0.0 0.797766
- 2 2 0.7071067 0.484123
- 10 2 0.7071067 -0.204789
- 20 2 0.7071067 0.910208
- 2 2 0.0 0.968246
- 10 2 0.0 0.804785
- 20 2 0.0 -0.799672
- 10 10 0.7071067 0.042505
- 20 10 0.7071067 -0.707252
- 10 10 0.0 1.360172
- 20 10 0.0 -0.853705
- Jacobian Elliptic Function
- 20 Values
- 0.0 0.1 0.099833
- 0.0 0.2 0.19867
- 0.0 0.5 0.47943
- 0.0 1.0 0.84147
- 0.0 2.0 0.90930
- 0.5 0.1 0.099751
- 0.5 0.2 0.19802
- 0.5 0.5 0.47075
- 0.5 1.0 0.80300
- 0.5 2.0 0.99466
- 1.0 0.1 0.099668
- 1.0 0.2 0.19738
- 1.0 0.5 0.46212
- 1.0 1.0 0.76159
- 1.0 2.0 0.96403
- 1.0 4.0 0.99933
- 1.0 -0.2 -0.19738
- 1.0 -0.5 -0.46212
- 1.0 -1.0 -0.76159
- 1.0 -2.0 -0.96403
-