S Chapter Contents (PDF version)
S Chapter Introduction
NAG Library Manual

NAG Library Chapter Contents

S – Approximations of Special Functions

S Chapter Introduction

Routine
Name
Mark of
Introduction

Purpose
S01BAF
Example Text
Example Data
14 nagf_specfun_log_shifted
ln(1 + x)
S01EAF
Example Text
Example Data
14 nagf_specfun_exp_complex
Complex exponential, ez
S07AAF
Example Text
Example Data
1 nagf_specfun_tan
tanx
S09AAF
Example Text
Example Data
1 nagf_specfun_arcsin
arcsinx
S09ABF
Example Text
Example Data
3 nagf_specfun_arccos
arccosx
S10AAF
Example Text
Example Data
3 nagf_specfun_tanh
tanhx
S10ABF
Example Text
Example Data
4 nagf_specfun_sinh
sinhx
S10ACF
Example Text
Example Data
4 nagf_specfun_cosh
coshx
S11AAF
Example Text
Example Data
4 nagf_specfun_arctanh
arctanhx
S11ABF
Example Text
Example Data
4 nagf_specfun_arcsinh
arcsinhx
S11ACF
Example Text
Example Data
4 nagf_specfun_arccosh
arccoshx
S13AAF
Example Text
Example Data
Example Plot
1 nagf_specfun_integral_exp
Exponential integral E1(x)
S13ACF
Example Text
Example Data
2 nagf_specfun_integral_cos
Cosine integral Ci(x)
S13ADF
Example Text
Example Data
5 nagf_specfun_integral_sin
Sine integral Si(x)
S14AAF
Example Text
Example Data
1 nagf_specfun_gamma
Gamma function
S14ABF
Example Text
Example Data
8 nagf_specfun_gamma_log_real
Log gamma function, real argument
S14ACF
Example Text
Example Data
14 nagf_specfun_polygamma
ψ(x) - lnx
S14ADF
Example Text
Example Data
14 nagf_specfun_polygamma_deriv
Scaled derivatives of ψ(x)
S14AEF
Example Text
Example Data
20 nagf_specfun_psi_deriv_real
Polygamma function ψ(n)(x) for real x
S14AFF
Example Text
Example Data
20 nagf_specfun_psi_deriv_complex
Polygamma function ψ(n)(z) for complex z
S14AGF
Example Text
Example Data
21 nagf_specfun_gamma_log_complex
Logarithm of the gamma function lnΓ(z), complex argument
S14AHF
Example Text
Example Data
23 nagf_specfun_gamma_log_scaled_real
Scaled log gamma function
S14BAF
Example Text
Example Data
14 nagf_specfun_gamma_incomplete
Incomplete gamma functions P(a,x) and Q(a,x)
S15ABF
Example Text
Example Data
3 nagf_specfun_cdf_normal
Cumulative Normal distribution function P(x)
S15ACF
Example Text
Example Data
4 nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Q(x)
S15ADF
Example Text
Example Data
4 nagf_specfun_erfc_real
Complement of error function erfc(x)
S15AEF
Example Text
Example Data
4 nagf_specfun_erf_real
Error function erf(x)
S15AFF
Example Text
Example Data
7 nagf_specfun_dawson
Dawson's integral
S15AGF
Example Text
Example Data
22 nagf_specfun_erfcx_real
Scaled complement of error function, erfcx(x)
S15DDF
Example Text
Example Data
14 nagf_specfun_erfc_complex
Scaled complex complement of error function, exp( - z2)erfc( - iz)
S17ACF
Example Text
Example Data
1 nagf_specfun_bessel_y0_real
Bessel function Y0(x)
S17ADF
Example Text
Example Data
1 nagf_specfun_bessel_y1_real
Bessel function Y1(x)
S17AEF
Example Text
Example Data
5 nagf_specfun_bessel_j0_real
Bessel function J0(x)
S17AFF
Example Text
Example Data
5 nagf_specfun_bessel_j1_real
Bessel function J1(x)
S17AGF
Example Text
Example Data
8 nagf_specfun_airy_ai_real
Airy function Ai(x)
S17AHF
Example Text
Example Data
8 nagf_specfun_airy_bi_real
Airy function Bi(x)
S17AJF
Example Text
Example Data
8 nagf_specfun_airy_ai_deriv
Airy function Ai(x)
S17AKF
Example Text
Example Data
8 nagf_specfun_airy_bi_deriv
Airy function Bi(x)
S17ALF
Example Text
Example Data
20 nagf_specfun_bessel_zeros
Zeros of Bessel functions Jα(x), Jα(x), Yα(x) or Yα(x)
S17DCF
Example Text
Example Data
13 nagf_specfun_bessel_y_complex
Bessel functions Yν + a(z), real a0, complex z, ν = 0,1,2,
S17DEF
Example Text
Example Data
13 nagf_specfun_bessel_j_complex
Bessel functions Jν + a(z), real a0, complex z, ν = 0,1,2,
S17DGF
Example Text
Example Data
13 nagf_specfun_airy_ai_complex
Airy functions Ai(z) and Ai(z), complex z
S17DHF
Example Text
Example Data
13 nagf_specfun_airy_bi_complex
Airy functions Bi(z) and Bi(z), complex z
S17DLF
Example Text
Example Data
13 nagf_specfun_hankel_complex
Hankel functions Hν + a(j)(z), j = 1,2, real a0, complex z, ν=0,1,2,
S18ACF
Example Text
Example Data
1 nagf_specfun_bessel_k0_real
Modified Bessel function K0(x)
S18ADF
Example Text
Example Data
1 nagf_specfun_bessel_k1_real
Modified Bessel function K1(x)
S18AEF
Example Text
Example Data
5 nagf_specfun_bessel_i0_real
Modified Bessel function I0(x)
S18AFF
Example Text
Example Data
5 nagf_specfun_bessel_i1_real
Modified Bessel function I1(x)
S18CCF
Example Text
Example Data
10 nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function exK0(x)
S18CDF
Example Text
Example Data
10 nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function exK1(x)
S18CEF
Example Text
Example Data
10 nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e - |x|I0(x)
S18CFF
Example Text
Example Data
10 nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e - |x|I1(x)
S18DCF
Example Text
Example Data
13 nagf_specfun_bessel_k_complex
Modified Bessel functions Kν + a(z), real a0, complex z, ν = 0,1,2,
S18DEF
Example Text
Example Data
13 nagf_specfun_bessel_i_complex
Modified Bessel functions Iν + a(z), real a0, complex z, ν = 0,1,2,
S18GKF
Example Text
Example Data
21 nagf_specfun_bessel_j_seq_complex
Bessel function of the 1st kind Jα ± n(z)
S19AAF
Example Text
Example Data
11 nagf_specfun_kelvin_ber
Kelvin function berx
S19ABF
Example Text
Example Data
11 nagf_specfun_kelvin_bei
Kelvin function beix
S19ACF
Example Text
Example Data
11 nagf_specfun_kelvin_ker
Kelvin function kerx
S19ADF
Example Text
Example Data
11 nagf_specfun_kelvin_kei
Kelvin function keix
S20ACF
Example Text
Example Data
5 nagf_specfun_fresnel_s
Fresnel integral S(x)
S20ADF
Example Text
Example Data
5 nagf_specfun_fresnel_c
Fresnel integral C(x)
S21BAF
Example Text
8 nagf_specfun_ellipint_symm_1_degen
Degenerate symmetrised elliptic integral of 1st kind RC(x,y)
S21BBF
Example Text
8 nagf_specfun_ellipint_symm_1
Symmetrised elliptic integral of 1st kind RF(x,y,z)
S21BCF
Example Text
8 nagf_specfun_ellipint_symm_2
Symmetrised elliptic integral of 2nd kind RD(x,y,z)
S21BDF
Example Text
8 nagf_specfun_elliptic_symm_3
Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r)
S21BEF
Example Text
22 nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, F(φm)
S21BFF
Example Text
22 nagf_specfun_ellipint_legendre_2
Elliptic integral of 2nd kind, Legendre form, E (φm)
S21BGF
Example Text
22 nagf_specfun_ellipint_legendre_3
Elliptic integral of 3rd kind, Legendre form, Π (n ; φm)
S21BHF
Example Text
22 nagf_specfun_ellipint_complete_1
Complete elliptic integral of 1st kind, Legendre form, K (m)
S21BJF
Example Text
22 nagf_specfun_ellipint_complete_2
Complete elliptic integral of 2nd kind, Legendre form, E (m)
S21CAF
Example Text
Example Data
15 nagf_specfun_jacellip_real
Jacobian elliptic functions sn, cn and dn of real argument
S21CBF
Example Text
Example Data
20 nagf_specfun_jacellip_complex
Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF
Example Text
Example Data
20 nagf_specfun_jactheta_real
Jacobian theta functions θk(x,q) of real argument
S21DAF
Example Text
Example Data
20 nagf_specfun_ellipint_general_2
General elliptic integral of 2nd kind F(z,k,a,b) of complex argument
S22AAF
Example Text
Example Data
20 nagf_specfun_legendre_p
Legendre functions of 1st kind Pnm(x) or Pnm(x)
S30AAF
Example Text
Example Data
22 nagf_specfun_opt_bsm_price
Black–Scholes–Merton option pricing formula
S30ABF
Example Text
Example Data
22 nagf_specfun_opt_bsm_greeks
Black–Scholes–Merton option pricing formula with Greeks
S30BAF
Example Text
Example Data
22 nagf_specfun_opt_lookback_fls_price
Floating-strike lookback option pricing formula
S30BBF
Example Text
Example Data
22 nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks
S30CAF
Example Text
Example Data
22 nagf_specfun_opt_binary_con_price
Binary option: cash-or-nothing pricing formula
S30CBF
Example Text
Example Data
22 nagf_specfun_opt_binary_con_greeks
Binary option: cash-or-nothing pricing formula with Greeks
S30CCF
Example Text
Example Data
22 nagf_specfun_opt_binary_aon_price
Binary option: asset-or-nothing pricing formula
S30CDF
Example Text
Example Data
22 nagf_specfun_opt_binary_aon_greeks
Binary option: asset-or-nothing pricing formula with Greeks
S30FAF
Example Text
Example Data
22 nagf_specfun_opt_barrier_std_price
Standard barrier option pricing formula
S30JAF
Example Text
Example Data
22 nagf_specfun_opt_jumpdiff_merton_price
Jump-diffusion, Merton's model, option pricing formula
S30JBF
Example Text
Example Data
22 nagf_specfun_opt_jumpdiff_merton_greeks
Jump-diffusion, Merton's model, option pricing formula with Greeks
S30NAF
Example Text
Example Data
22 nagf_specfun_opt_heston_price
Heston's model option pricing formula
S30NBF
Example Text
Example Data
23 nagf_specfun_opt_heston_greeks
Heston's model option pricing formula with Greeks
S30QCF
Example Text
Example Data
22 nagf_specfun_opt_amer_bs_price
American option: Bjerksund and Stensland pricing formula
S30SAF
Example Text
Example Data
22 nagf_specfun_opt_asian_geom_price
Asian option: geometric continuous average rate pricing formula
S30SBF
Example Text
Example Data
22 nagf_specfun_opt_asian_geom_greeks
Asian option: geometric continuous average rate pricing formula with Greeks

S Chapter Contents (PDF version)
S Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011