s - Approximations of Special Functions

Chapter Introduction
s10aac	nag_tanh Hyperbolic tangent, tanh x
s10abc	nag_sinh Hyperbolic sine, sinh x
s10acc	nag_cosh Hyperbolic cosine, cosh x
s11aac	nag_arctanh Inverse hyperbolic tangent, arctanh x
s11abc	nag_arcsinh Inverse hyperbolic sine, arcsinh x
s11acc	nag_arccosh Inverse hyperbolic cosine, arccosh x
s13aac	nag_exp_integral Exponential integral E1 (x)
s13acc	nag_cos_integral Cosine integral Ci(x)
s13adc	nag_sin_integral Sine integral Si(x)
s14aac	nag_gamma Gamma function gamma(x)
s14abc	nag_log_gamma Log Gamma function ln(gamma(x))
s14aec	nag_real_polygamma Derivative of the psi function psi(x)
s14afc	nag_complex_polygamma Derivative of the psi function psi(z)
s14bac	nag_incomplete_gamma Incomplete gamma functions P(a,x) and Q(a,x)
s15abc	nag_cumul_normal Cumulative normal distribution function, P(x)
s15acc	nag_cumul_normal_complem Complement of cumulative normal distribution function, Q(x)
s15adc	nag_erfc Complement of error function, erfc x
s15aec	nag_erf Error function, erf x
s17acc	nag_bessel_y0 Bessel function Y0 (x)
s17adc	nag_bessel_y1 Bessel function Y1 (x)
s17aec	nag_bessel_j0 Bessel function J0 (x)
s17afc	nag_bessel_j1 Bessel function J1 (x)
s17agc	nag_airy_ai Airy function Ai(x)
s17ahc	nag_airy_bi Airy function Bi(x)
s17ajc	nag_airy_ai_deriv Airy function Ai'(x)
s17akc	nag_airy_bi_deriv Airy function Bi'(x)
s17alc	nag_bessel_zeros Zeros of Bessel functions Jalpha(x), J'alpha(x), Yalpha(x) or Y'alpha(x)
s18acc	nag_bessel_k0 Modified Bessel function K0 (x)
s18adc	nag_bessel_k1 Modified Bessel function K1 (x)
s18aec	nag_bessel_i0 Modified Bessel function I0 (x)
s18afc	nag_bessel_i1 Modified Bessel function I1 (x)
s18ccc	nag_bessel_k0_scaled Scaled modified Bessel function ex K0 (x)
s18cdc	nag_bessel_k1_scaled Scaled modified Bessel function ex K1 (x)
s18cec	nag_bessel_i0_scaled Scaled modified Bessel function e-|x| I0 (x)
s18cfc	nag_bessel_i1_scaled Scaled modified Bessel function e-|x| I1 (x)
s18ecc	nag_bessel_i_nu_scaled Scaled modified Bessel function e-x Inu/4(x)
s18edc	nag_bessel_k_nu_scaled Scaled modified Bessel function ex Knu/4(x)
s18eec	nag_bessel_i_nu Modified Bessel function Inu/4(x)
s18efc	nag_bessel_k_nu Modified Bessel function Knu/4(x)
s18egc	nag_bessel_k_alpha Modified Bessel functions Kalpha+n(x) for real x > 0, selected values of alpha ≥ 0 and n = 0,1,...,N
s18ehc	nag_bessel_k_alpha_scaled Scaled modified Bessel functions functions Kalpha+n(x) for real x > 0, selected values of alpha ≥ 0 and n = 0,1,...,N
s18ejc	nag_bessel_i_alpha Modified Bessel functions Ialpha+n-1(x) or Ialpha-n+1(x) for real x ≠ 0, non-negative alpha < 1 and n = 1,2,...,|N|+1
s18ekc	nag_bessel_j_alpha Bessel functions Jalpha+n-1(x) or Jalpha-n+1(x) for real x ≠ 0, non-negative alpha < 1 and n = 1,2,...,|N|+1
s19aac	nag_kelvin_ber Kelvin function ber x
s19abc	nag_kelvin_bei Kelvin function bei x
s19acc	nag_kelvin_ker Kelvin function ker x
s19adc	nag_kelvin_kei Kelvin function kei x
s20acc	nag_fresnel_s Fresnel integral S(x)
s20adc	nag_fresnel_c Fresnel integral C(x)
s21bac	nag_elliptic_integral_rc Degenerate symmetrised elliptic integral of 1st kind RC (x,y)
s21bbc	nag_elliptic_integral_rf Symmetrised elliptic integral of 1st kind RF (x,y,z)
s21bcc	nag_elliptic_integral_rd Symmetrised elliptic integral of 2nd kind RD (x,y,z)
s21bdc	nag_elliptic_integral_rj Symmetrised elliptic integral of 3rd kind RJ (x,y,z,r)
s21cbc	nag_jacobian_elliptic Jacobian elliptic functions sn, cn and dn with complex arguments
s21ccc	nag_jacobian_theta Jacobian theta functions with real arguments
s21dac	nag_elliptic_integral_f Elliptic integrals of the second kind with complex arguments
s22aac	nag_legendre_p Legendre and associated Legendre functions of the first kind with real arguments