NAG Fortran Library

Chapter S

Approximations of Special Functions

Chapter Introduction
S01BAF    ln (1+x)
S01EAF    Complex exponential, e^z
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    ψ (x) - ln x
S14ADF    Scaled derivatives of ψ (x)
S14AEF    Polygamma function ψ(n)(x) for real x
S14AFF    Polygamma function ψ(n)(z) for complex z
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)
S17ALF    Zeros of Bessel functions Jα(x), J'α(x), Yα(x) or Y'α(x)
S17DCF    Bessel functions Yν+a(z), real a ≥ 0, complex z, ν =0,1, 2,...
S17DEF    Bessel functions Jν+a(z), real a ≥ 0, complex z, ν =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 Hν+a(j)(z), j=1,2, real a ≥ 0, complex z, ν =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 Kν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
S18DEF    Modified Bessel functions Iν+a(z), real a ≥ 0, complex z, ν =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 of real argument
S21CBF    Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF    Jacobian theta functions θk (x,q) of real argument
S21DAF    General elliptic integral of 2nd kind F(z,k',a,b) of complex argument
S22AAF    Legendre functions of 1st kind Pnm (x) or Pnmx

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© The Numerical Algorithms Group Ltd, Oxford UK. 2001