NAG Fortran Library

S – Approximations of Special Functions

S Chapter Introduction

Routine
Name
Mark of
Introduction

Purpose
S01BAF Example Text Example Data 14 ln (1+x)
S01EAF Example Text Example Data 14 Complex exponential, ez
S07AAF Example Text Example Data 1 tan x
S09AAF Example Text Example Data 1 arcsin x
S09ABF Example Text Example Data 3 arccos x
S10AAF Example Text Example Data 3 tanh x
S10ABF Example Text Example Data 4 sinh x
S10ACF Example Text Example Data 4 cosh x
S11AAF Example Text Example Data 4 arctanh x
S11ABF Example Text Example Data 4 arcsinh x
S11ACF Example Text Example Data 4 arccosh x
S13AAF Example Text Example Data 1 Exponential integral E1 (x)
S13ACF Example Text Example Data 2 Cosine integral Ci(x)
S13ADF Example Text Example Data 5 Sine integral Si(x)
S14AAF Example Text Example Data 1 Gamma function
S14ABF Example Text Example Data 8 Log Gamma function
S14ACF Example Text Example Data 14 ψ (x) - ln x
S14ADF Example Text Example Data 14 Scaled derivatives of ψ (x)
S14AEF Example Text Example Data 20 Polygamma function ψ(n)(x) for real x
S14AFF Example Text Example Data 20 Polygamma function ψ(n)(z) for complex z
S14BAF Example Text Example Data 14 Incomplete Gamma functions P(a,x) and Q(a,x)
S15ABF Example Text Example Data 3 Cumulative Normal distribution function P(x)
S15ACF Example Text Example Data 4 Complement of cumulative Normal distribution function Q(x)
S15ADF Example Text Example Data 4 Complement of error function erfc(x)
S15AEF Example Text Example Data 4 Error function erf(x)
S15AFF Example Text Example Data 7 Dawson's integral
S15DDF Example Text Example Data 14 Scaled complex complement of error function, exp(-z2) erfc(-iz)
S17ACF Example Text Example Data 1 Bessel function Y0 (x)
S17ADF Example Text Example Data 1 Bessel function Y1 (x)
S17AEF Example Text Example Data 5 Bessel function J0 (x)
S17AFF Example Text Example Data 5 Bessel function J1 (x)
S17AGF Example Text Example Data 8 Airy function Ai(x)
S17AHF Example Text Example Data 8 Airy function Bi(x)
S17AJF Example Text Example Data 8 Airy function Ai'(x)
S17AKF Example Text Example Data 8 Airy function Bi'(x)
S17ALF Example Text Example Data 20 Zeros of Bessel functions Jα(x), J'α(x), Yα(x) or Y'α(x)
S17DCF Example Text Example Data 13 Bessel functions Yν+a(z), real a ≥ 0, complex z, ν =0,1, 2,...
S17DEF Example Text Example Data 13 Bessel functions Jν+a(z), real a ≥ 0, complex z, ν =0,1, 2,...
S17DGF Example Text Example Data 13 Airy functions Ai(z) and Ai'(z) , complex z
S17DHF Example Text Example Data 13 Airy functions Bi(z) and Bi'(z) , complex z
S17DLF Example Text Example Data 13 Hankel functions Hν+a(j)(z), j=1,2, real a ≥ 0, complex z, ν =0,1,2,...
S18ACF Example Text Example Data 1 Modified Bessel function K0 (x)
S18ADF Example Text Example Data 1 Modified Bessel function K1 (x)
S18AEF Example Text Example Data 5 Modified Bessel function I0 (x)
S18AFF Example Text Example Data 5 Modified Bessel function I1(x)
S18CCF Example Text Example Data 10 Modified Bessel function exK0(x)
S18CDF Example Text Example Data 10 Modified Bessel function exK1(x)
S18CEF Example Text Example Data 10 Modified Bessel function e-|x|I0(x)
S18CFF Example Text Example Data 10 Modified Bessel function e-|x|I1(x)
S18DCF Example Text Example Data 13 Modified Bessel functions Kν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
S18DEF Example Text Example Data 13 Modified Bessel functions Iν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
S19AAF Example Text Example Data 11 Kelvin function ber x
S19ABF Example Text Example Data 11 Kelvin function bei x
S19ACF Example Text Example Data 11 Kelvin function ker x
S19ADF Example Text Example Data 11 Kelvin function kei x
S20ACF Example Text Example Data 5 Fresnel integral S(x)
S20ADF Example Text Example Data 5 Fresnel integral C(x)
S21BAF Example Text 8 Degenerate symmetrised elliptic integral of 1st kind RC(x,y)
S21BBF Example Text 8 Symmetrised elliptic integral of 1st kind RF(x,y,z)
S21BCF Example Text 8 Symmetrised elliptic integral of 2nd kind RD(x,y,z)
S21BDF Example Text 8 Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r)
S21CAF Example Text Example Data 15 Jacobian elliptic functions sn, cn and dn of real argument
S21CBF Example Text Example Data 20 Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF Example Text Example Data 20 Jacobian theta functions θk (x,q) of real argument
S21DAF Example Text Example Data 20 General elliptic integral of 2nd kind F(z,k',a,b) of complex argument
S22AAF Example Text Example Data 20 Legendre functions of 1st kind Pnm (x) or Pnm(x)

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© The Numerical Algorithms Group Ltd, Oxford UK. 2002