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