# S - Approximations of Special Functions

 Chapter Introduction S01BAF ln(1 + x) S01EAF Complex exponential, ez S07AAF tan x S09AAF arcsin x S09ABF arccos x S10AAF tanh x S10ABF sinh x S10ACF cosh x S11AAF arctanh x S11ABF arcsinh x S11ACF arccosh x S13AAF Exponential integral E1(x) S13ACF Cosine integral Ci(x) S13ADF Sine integral Si(x) S14AAF Gamma function S14ABF Log Gamma function S14ACF psi (x) - ln x S14ADF Scaled derivatives of psi(x) S14BAF Incomplete Gamma functions P(a,x) and Q(a,x) S15ABF Cumulative normal distribution function P(x) S15ACF Complement of cumulative normal distribution function Q(x) S15ADF Complement of error function erfc(x) S15AEF Error function erf(x) S15AFF Dawson's integral S15DDF Scaled complex complement of error function, exp(-z2)erfc(-iz) S17ACF Bessel function Y0(x) S17ADF Bessel function Y1(x) S17AEF Bessel function J0(x) S17AFF Bessel function J1(x) S17AGF Airy function Ai(x) S17AHF Airy function Bi(x) S17AJF Airy function Ai'(x) S17AKF Airy function Bi'(x) S17DCF Bessel functions Ynu+a(z), real a >= 0, complex z, nu = 0,1, 2,... S17DEF Bessel functions Jnu+a(z), real a >= 0, complex z, nu = 0,1, 2,... S17DGF Airy functions Ai(z) and Ai'(z), complex z S17DHF Airy functions Bi(z) and Bi'(z), complex z S17DLF Hankel functions Hnu+a(j)(z), j = 1,2, real a >= 0, complex z, nu = 0,1,2,... S18ACF Modified Bessel function K0(x) S18ADF Modified Bessel function K1(x) S18AEF Modified Bessel function I0(x) S18AFF Modified Bessel function I1(x) S18CCF Modified Bessel function exK0(x) S18CDF Modified Bessel function exK1(x) S18CEF Modified Bessel function e-|x|I0(x) S18CFF Modified Bessel function e-|x|I1(x) S18DCF Modified Bessel functions Knu+a(z), real a >= 0, complex z, nu = 0,1,2,... S18DEF Modified Bessel functions Inu+a(z), real a >= 0, complex z, nu = 0,1,2,... S19AAF Kelvin function ber x S19ABF Kelvin function bei x S19ACF Kelvin function ker x S19ADF Kelvin function kei x S20ACF Fresnel integral S(x) S20ADF Fresnel integral C(x) S21BAF Degenerate symmetrised elliptic integral of 1st kind RC(x,y) S21BBF Symmetrised elliptic integral of 1st kind RF(x,y,z) S21BCF Symmetrised elliptic integral of 2nd kind RD(x,y,z) S21BDF Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r) S21CAF Jacobian elliptic functions sn, cn and dn

© The Numerical Algorithms Group Ltd, Oxford UK. 1999