Chapter Introduction (pdf version)
NAG C Library Manual

s – Approximations of Special Functions

s Chapter Introduction
Routine
Name
Mark of
Introduction

Purpose
s01bac
Example Text
Example Data
7 nag_shifted_log
ln(1+x)
s10aac
Example Text
Example Data
1 nag_tanh
Hyperbolic tangent, tanh x
s10abc
Example Text
Example Data
1 nag_sinh
Hyperbolic sine, sinh x
s10acc
Example Text
Example Data
1 nag_cosh
Hyperbolic cosine, cosh x
s11aac
Example Text
Example Data
1 nag_arctanh
Inverse hyperbolic tangent, arctanh x
s11abc
Example Text
Example Data
1 nag_arcsinh
Inverse hyperbolic sine, arcsinh x
s11acc
Example Text
Example Data
1 nag_arccosh
Inverse hyperbolic cosine, arccosh x
s13aac
Example Text
Example Data
1 nag_exp_integral
Exponential integral E1(x)
s13acc
Example Text
Example Data
1 nag_cos_integral
Cosine integral Ci(x)
s13adc
Example Text
Example Data
1 nag_sin_integral
Sine integral Si(x)
s14aac
Example Text
Example Data
1 nag_gamma
Gamma function Γ(x)
s14abc
Example Text
Example Data
1 nag_log_gamma
Log Gamma function ln(Γ(x))
s14acc
Example Text
Example Data
7 nag_polygamma_fun
ψ(x)-lnx
s14adc
Example Text
Example Data
7 nag_polygamma_deriv
Scaled derivatives of ψ(x)
s14aec
Example Text
Example Data
6 nag_real_polygamma
Derivative of the psi function ψ(x)
s14afc
Example Text
Example Data
6 nag_complex_polygamma
Derivative of the psi function ψ(z)
s14agc
Example Text
Example Data
7 nag_complex_log_gamma
Logarithm of the Gamma function lnΓ(z)
s14bac
Example Text
Example Data
1 nag_incomplete_gamma
Incomplete Gamma functions P(a,x) and Q(a,x)
s15abc
Example Text
Example Data
1 nag_cumul_normal
Cumulative Normal distribution function P(x)
s15acc
Example Text
Example Data
1 nag_cumul_normal_complem
Complement of cumulative Normal distribution function Q(x)
s15adc
Example Text
Example Data
1 nag_erfc
Complement of error function erfc(x)
s15aec
Example Text
Example Data
1 nag_erf
Error function erf(x)
s15afc
Example Text
Example Data
7 nag_dawson
Dawson's integral
s15ddc
Example Text
Example Data
7 nag_complex_erfc
Scaled complex complement of error function, exp(-z2)erfc(-iz)
s17acc
Example Text
Example Data
1 nag_bessel_y0
Bessel function Y0(x)
s17adc
Example Text
Example Data
1 nag_bessel_y1
Bessel function Y1(x)
s17aec
Example Text
Example Data
1 nag_bessel_j0
Bessel function J0(x)
s17afc
Example Text
Example Data
1 nag_bessel_j1
Bessel function J1(x)
s17agc
Example Text
Example Data
1 nag_airy_ai
Airy function Ai(x)
s17ahc
Example Text
Example Data
1 nag_airy_bi
Airy function Bi(x)
s17ajc
Example Text
Example Data
1 nag_airy_ai_deriv
Airy function Ai(x)
s17akc
Example Text
Example Data
1 nag_airy_bi_deriv
Airy function Bi(x)
s17alc
Example Text
Example Data
6 nag_bessel_zeros
Zeros of Bessel functions Jα(x), Jα(x), Yα(x) or Yα(x)
s17dcc
Example Text
Example Data
7 nag_complex_bessel_y
Bessel functions Yν+a(z), real a0, complex z, ν=0,1,2,
s17dec
Example Text
Example Data
7 nag_complex_bessel_j
Bessel functions Jν+a(z), real a0, complex z, ν=0,1,2,
s17dgc
Example Text
Example Data
7 nag_complex_airy_ai
Airy functions Ai(z) and Ai(z), complex z
s17dhc
Example Text
Example Data
7 nag_complex_airy_bi
Airy functions Bi(z) and Bi(z), complex z
s17dlc
Example Text
Example Data
7 nag_complex_hankel
Hankel functions Hν+a(j)(z), j=1,2, real a0, complex z, ν=0,1,2,
s18acc
Example Text
Example Data
1 nag_bessel_k0
Modified Bessel function K0(x)
s18adc
Example Text
Example Data
1 nag_bessel_k1
Modified Bessel function K1(x)
s18aec
Example Text
Example Data
1 nag_bessel_i0
Modified Bessel function I0(x)
s18afc
Example Text
Example Data
1 nag_bessel_i1
Modified Bessel function I1(x)
s18ccc
Example Text
Example Data
2 nag_bessel_k0_scaled
Scaled modified Bessel function exK0(x)
s18cdc
Example Text
Example Data
2 nag_bessel_k1_scaled
Scaled modified Bessel function exK1(x)
s18cec
Example Text
Example Data
2 nag_bessel_i0_scaled
Scaled modified Bessel function e-|x|I0(x)
s18cfc
Example Text
Example Data
2 nag_bessel_i1_scaled
Scaled modified Bessel function e-|x|I1(x)
s18dcc
Example Text
Example Data
7 nag_complex_bessel_k
Modified Bessel functions Kν+a(z), real a0, complex z, ν=0,1,2,
s18dec
Example Text
Example Data
7 nag_complex_bessel_i
Modified Bessel functions Iν+a(z), real a0, complex z, ν=0,1,2,
s18ecc
Example Text
Example Data
6 nag_bessel_i_nu_scaled
Scaled modified Bessel function e-x Iν/4(x)
s18edc
Example Text
Example Data
6 nag_bessel_k_nu_scaled
Scaled modified Bessel function exKν/4(x)
s18eec
Example Text
Example Data
6 nag_bessel_i_nu
Modified Bessel function Iν/4(x)
s18efc
Example Text
Example Data
6 nag_bessel_k_nu
Modified Bessel function Kν/4(x)
s18egc
Example Text
Example Data
6 nag_bessel_k_alpha
Modified Bessel functions Kα+n(x) for real x>0, selected values of α0 and n=0,1,,n
s18ehc
Example Text
Example Data
6 nag_bessel_k_alpha_scaled
Scaled modified Bessel functions Kα+n(x) for real x>0, selected values of α 0 and n=0,1,,N
s18ejc
Example Text
Example Data
6 nag_bessel_i_alpha
Modified Bessel functions Iα+n-1(x) or Iα-n+1(x) for real x0, non-negative α<1 and n=1,2,,|N|+1
s18ekc
Example Text
Example Data
6 nag_bessel_j_alpha
Bessel functions Jα+n-1(x) or Jα-n+1(x) for real x0, non-negative α<1 and n=1,2,,|N|+1
s18gkc
Example Text
Example Data
7 nag_complex_bessel_j_seq
Bessel function of the 1st kind Jαn(z)
s19aac
Example Text
Example Data
1 nag_kelvin_ber
Kelvin function berx
s19abc
Example Text
Example Data
1 nag_kelvin_bei
Kelvin function beix
s19acc
Example Text
Example Data
1 nag_kelvin_ker
Kelvin function kerx
s19adc
Example Text
Example Data
1 nag_kelvin_kei
Kelvin function keix
s20acc
Example Text
Example Data
1 nag_fresnel_s
Fresnel integral S(x)
s20adc
Example Text
Example Data
1 nag_fresnel_c
Fresnel integral C(x)
s21bac
Example Text
1 nag_elliptic_integral_rc
Degenerate symmetrised elliptic integral of 1st kind RC(x,y)
s21bbc
Example Text
1 nag_elliptic_integral_rf
Symmetrised elliptic integral of 1st kind RF(x,y,z)
s21bcc
Example Text
1 nag_elliptic_integral_rd
Symmetrised elliptic integral of 2nd kind RD(x,y,z)
s21bdc
Example Text
1 nag_elliptic_integral_rj
Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r)
s21cac
Example Text
Example Data
7 nag_real_jacobian_elliptic
Jacobian elliptic functions sn, cn and dn of real argument
s21cbc
Example Text
Example Data
6 nag_jacobian_elliptic
Jacobian elliptic functions sn, cn and dn of complex argument
s21ccc
Example Text
Example Data
6 nag_jacobian_theta
Jacobian theta functions with real arguments
s21dac
Example Text
Example Data
6 nag_elliptic_integral_f
Elliptic integrals of the second kind with complex arguments
s22aac
Example Text
Example Data
6 nag_legendre_p
Legendre and associated Legendre functions of the first kind with real arguments

Chapter Introduction (pdf version)
NAG C Library Manual

The Numerical Algorithms Group Ltd, Oxford, UK. 2005