NAG C Library Manual, Mark 7 : s Chapter Contents

s – Approximations of Special Functions

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) - ln x
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 ln Γ (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 J_α(x), J'_α(x), Y_α(x) or Y'_α(x)
s17dcc Example Text Example Data	7	nag_complex_bessel_y Bessel functions Y_ν+a(z), real a ≥ 0, complex z, ν =0,1, 2,...
s17dec Example Text Example Data	7	nag_complex_bessel_j Bessel functions J_ν+a(z), real a ≥ 0, 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 H_ν+a^(j)(z), j=1,2, real a ≥ 0, 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 e^xK₀(x)
s18cdc Example Text Example Data	2	nag_bessel_k1_scaled Scaled modified Bessel function e^xK₁(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 K_ν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
s18dec Example Text Example Data	7	nag_complex_bessel_i Modified Bessel functions I_ν+a(z), real a ≥ 0, complex z, ν =0,1,2,...
s18ecc Example Text Example Data	6	nag_bessel_i_nu_scaled Scaled modified Bessel function e^-x I_ν/4 (x)
s18edc Example Text Example Data	6	nag_bessel_k_nu_scaled Scaled modified Bessel function e^x K_ν/4 (x)
s18eec Example Text Example Data	6	nag_bessel_i_nu Modified Bessel function I_ν/4 (x)
s18efc Example Text Example Data	6	nag_bessel_k_nu Modified Bessel function K_ν/4 (x)
s18egc Example Text Example Data	6	nag_bessel_k_alpha Modified Bessel functions K_α+n (x) for real x > 0, selected values of α ≥ 0 and n = 0,1,...,N
s18ehc Example Text Example Data	6	nag_bessel_k_alpha_scaled Scaled modified Bessel functions K_α+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 I_{α +n-1} (x) or I_{α -n+1} (x) for real x ≠ 0, non-negative α < 1 and n = 1,2,...,\|N\|+1
s18ekc Example Text Example Data	6	nag_bessel_j_alpha Bessel functions J_{α +n-1} (x) or J_{α -n+1} (x) for real x ≠ 0, 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 J_{α ± n}(z)
s19aac Example Text Example Data	1	nag_kelvin_ber Kelvin function ber x
s19abc Example Text Example Data	1	nag_kelvin_bei Kelvin function bei x
s19acc Example Text Example Data	1	nag_kelvin_ker Kelvin function ker x
s19adc Example Text Example Data	1	nag_kelvin_kei Kelvin function kei x
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 R_C(x,y)
s21bbc Example Text	1	nag_elliptic_integral_rf Symmetrised elliptic integral of 1st kind R_F(x,y,z)
s21bcc Example Text	1	nag_elliptic_integral_rd Symmetrised elliptic integral of 2nd kind R_D(x,y,z)
s21bdc Example Text	1	nag_elliptic_integral_rj Symmetrised elliptic integral of 3rd kind R_J(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

NAG C Library Manual