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

NAG Library Chapter Contents

S – Approximations of Special Functions


S Chapter Introduction – a description of the Chapter and an overview of the algorithms available

Routine
Name
Mark of
Introduction

Purpose
S01BAF
Example Text
Example Data
14 nagf_specfun_log_shifted
ln1+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 E1x
S13ACF
Example Text
Example Data
Example Plot
2 nagf_specfun_integral_cos
Cosine integral Cix
S13ADF
Example Text
Example Data
Example Plot
5 nagf_specfun_integral_sin
Sine integral Six
S14AAF
Example Text
Example Data
Example Plot
1 nagf_specfun_gamma
Gamma function
S14ABF
Example Text
Example Data
Example Plot
8 nagf_specfun_gamma_log_real
Log gamma function, real argument
S14ACF
Example Text
Example Data
Example Plot
14 nagf_specfun_polygamma
ψx-lnx
S14ADF
Example Text
Example Data
14 nagf_specfun_polygamma_deriv
Scaled derivatives of ψx
S14AEF
Example Text
Example Data
20 nagf_specfun_psi_deriv_real
Polygamma function ψnx for real x
S14AFF
Example Text
Example Data
20 nagf_specfun_psi_deriv_complex
Polygamma function ψnz for complex z
S14AGF
Example Text
Example Data
21 nagf_specfun_gamma_log_complex
Logarithm of the gamma function lnΓz, complex argument
S14AHF
Example Text
Example Data
Example Plot
23 nagf_specfun_gamma_log_scaled_real
Scaled log gamma function
S14BAF
Example Text
Example Data
Example Plot
14 nagf_specfun_gamma_incomplete
Incomplete gamma functions Pa,x and Qa,x
S14CBF
Example Text
Example Data
24 nagf_specfun_beta_log_real
Logarithm of the beta function lnBa,b
S14CCF
Example Text
Example Data
24 nagf_specfun_beta_incomplete
Incomplete beta function Ixa,b and its complement 1-Ix
S15ABF
Example Text
Example Data
3 nagf_specfun_cdf_normal
Cumulative Normal distribution function Px
S15ACF
Example Text
Example Data
4 nagf_specfun_compcdf_normal
Complement of cumulative Normal distribution function Qx
S15ADF
Example Text
Example Data
4 nagf_specfun_erfc_real
Complement of error function erfcx
S15AEF
Example Text
Example Data
4 nagf_specfun_erf_real
Error function erfx
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, erfcxx
S15DDF
Example Text
Example Data
14 nagf_specfun_erfc_complex
Scaled complex complement of error function, exp-z2erfc-iz
S17ACF
Example Text
Example Data
Example Plot
1 nagf_specfun_bessel_y0_real
Bessel function Y0x
S17ADF
Example Text
Example Data
Example Plot
1 nagf_specfun_bessel_y1_real
Bessel function Y1x
S17AEF
Example Text
Example Data
Example Plot
5 nagf_specfun_bessel_j0_real
Bessel function J0x
S17AFF
Example Text
Example Data
Example Plot
5 nagf_specfun_bessel_j1_real
Bessel function J1x
S17AGF
Example Text
Example Data
Example Plot
8 nagf_specfun_airy_ai_real
Airy function Aix
S17AHF
Example Text
Example Data
Example Plot
8 nagf_specfun_airy_bi_real
Airy function Bix
S17AJF
Example Text
Example Data
Example Plot
8 nagf_specfun_airy_ai_deriv
Airy function Aix
S17AKF
Example Text
Example Data
Example Plot
8 nagf_specfun_airy_bi_deriv
Airy function Bix
S17ALF
Example Text
Example Data
20 nagf_specfun_bessel_zeros
Zeros of Bessel functions Jαx, Jαx, Yαx or Yαx
S17AQF
Example Text
Example Data
24 nagf_specfun_bessel_y0_real_vector
Bessel function vectorized Y0x
S17ARF
Example Text
Example Data
24 nagf_specfun_bessel_y1_real_vector
Bessel function vectorized Y1x
S17ASF
Example Text
Example Data
24 nagf_specfun_bessel_j0_real_vector
Bessel function vectorized J0x
S17ATF
Example Text
Example Data
24 nagf_specfun_bessel_j1_real_vector
Bessel function vectorized J1x
S17AUF
Example Text
Example Data
24 nagf_specfun_airy_ai_real_vector
Airy function vectorized Aix
S17AVF
Example Text
Example Data
24 nagf_specfun_airy_bi_real_vector
Airy function vectorized Bix
S17AWF
Example Text
Example Data
24 nagf_specfun_airy_ai_deriv_vector
Derivatives of the Airy function, vectorized Aix
S17AXF
Example Text
Example Data
24 nagf_specfun_airy_bi_deriv_vector
Derivatives of the Airy function, vectorized Bix
S17DCF
Example Text
Example Data
13 nagf_specfun_bessel_y_complex
Bessel functions Yν+az, real a0, complex z, ν=0,1,2,
S17DEF
Example Text
Example Data
13 nagf_specfun_bessel_j_complex
Bessel functions Jν+az, real a0, complex z, ν=0,1,2,
S17DGF
Example Text
Example Data
13 nagf_specfun_airy_ai_complex
Airy functions Aiz and Aiz, complex z
S17DHF
Example Text
Example Data
13 nagf_specfun_airy_bi_complex
Airy functions Biz and Biz, complex z
S17DLF
Example Text
Example Data
13 nagf_specfun_hankel_complex
Hankel functions Hν+ajz, j=1,2, real a0, complex z, ν=0,1,2,
S18ACF
Example Text
Example Data
Example Plot
1 nagf_specfun_bessel_k0_real
Modified Bessel function K0x
S18ADF
Example Text
Example Data
Example Plot
1 nagf_specfun_bessel_k1_real
Modified Bessel function K1x
S18AEF
Example Text
Example Data
Example Plot
5 nagf_specfun_bessel_i0_real
Modified Bessel function I0x
S18AFF
Example Text
Example Data
Example Plot
5 nagf_specfun_bessel_i1_real
Modified Bessel function I1x
S18AQF
Example Text
Example Data
24 nagf_specfun_bessel_k0_real_vector
Modified Bessel function vectorized K0x
S18ARF
Example Text
Example Data
24 nagf_specfun_bessel_k1_real_vector
Modified Bessel function vectorized K1x
S18ASF
Example Text
Example Data
24 nagf_specfun_bessel_i0_real_vector
Modified Bessel function vectorized I0x
S18ATF
Example Text
Example Data
24 nagf_specfun_bessel_i1_real_vector
Modified Bessel function vectorized I1x
S18CCF
Example Text
Example Data
10 nagf_specfun_bessel_k0_scaled
Scaled modified Bessel function exK0x
S18CDF
Example Text
Example Data
10 nagf_specfun_bessel_k1_scaled
Scaled modified Bessel function exK1x
S18CEF
Example Text
Example Data
10 nagf_specfun_bessel_i0_scaled
Scaled modified Bessel function e-xI0x
S18CFF
Example Text
Example Data
10 nagf_specfun_bessel_i1_scaled
Scaled modified Bessel function e-xI1x
S18CQF
Example Text
Example Data
24 nagf_specfun_bessel_k0_scaled_vector
Scaled modified Bessel function vectorized exK0x
S18CRF
Example Text
Example Data
24 nagf_specfun_bessel_k1_scaled_vector
Scaled modified Bessel function vectorized exK1x
S18CSF
Example Text
Example Data
24 nagf_specfun_bessel_i0_scaled_vector
Scaled modified Bessel function vectorized e-xI0x
S18CTF
Example Text
Example Data
24 nagf_specfun_bessel_i1_scaled_vector
Scaled modified Bessel function vectorized e-xI1x
S18DCF
Example Text
Example Data
13 nagf_specfun_bessel_k_complex
Modified Bessel functions Kν+az, real a0, complex z, ν=0,1,2,
S18DEF
Example Text
Example Data
13 nagf_specfun_bessel_i_complex
Modified Bessel functions Iν+az, 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±nz
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
S19ANF
Example Text
Example Data
24 nagf_specfun_kelvin_ber_vector
Kelvin function vectorized berx
S19APF
Example Text
Example Data
24 nagf_specfun_kelvin_bei_vector
Kelvin function vectorized beix
S19AQF
Example Text
Example Data
24 nagf_specfun_kelvin_ker_vector
Kelvin function vectorized kerx
S19ARF
Example Text
Example Data
24 nagf_specfun_kelvin_kei_vector
Kelvin function vectorized keix
S20ACF
Example Text
Example Data
Example Plot
5 nagf_specfun_fresnel_s
Fresnel integral Sx
S20ADF
Example Text
Example Data
Example Plot
5 nagf_specfun_fresnel_c
Fresnel integral Cx
S20AQF
Example Text
Example Data
24 nagf_specfun_fresnel_s_vector
Fresnel integral vectorized Sx
S20ARF
Example Text
Example Data
24 nagf_specfun_fresnel_c_vector
Fresnel integral vectorized Cx
S21BAF
Example Text
8 nagf_specfun_ellipint_symm_1_degen
Degenerate symmetrised elliptic integral of 1st kind RCx,y
S21BBF
Example Text
8 nagf_specfun_ellipint_symm_1
Symmetrised elliptic integral of 1st kind RFx,y,z
S21BCF
Example Text
8 nagf_specfun_ellipint_symm_2
Symmetrised elliptic integral of 2nd kind RDx,y,z
S21BDF
Example Text
8 nagf_specfun_ellipint_symm_3
Symmetrised elliptic integral of 3rd kind RJx,y,z,r
S21BEF
Example Text
Example Plot
22 nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, Fϕm
S21BFF
Example Text
Example Plot
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 θkx,q of real argument
S21DAF
Example Text
Example Data
20 nagf_specfun_ellipint_general_2
General elliptic integral of 2nd kind Fz,k,a,b of complex argument
S22AAF
Example Text
Example Data
20 nagf_specfun_legendre_p
Legendre functions of 1st kind Pnmx or Pnm¯x
S22BAF
Example Text
24 nagf_specfun_1f1_real
Real confluent hypergeometric function F 1 1 a;b;x
S22BBF
Example Text
24 nagf_specfun_1f1_real_scaled
Real confluent hypergeometric function F 1 1 a;b;x  in scaled form
S22BEF
Example Text
25 nagf_specfun_2f1_real
Real Gauss hypergeometric function F1 2 a,b;c;x
S22BFF
Example Text
25 nagf_specfun_2f1_real_scaled
Real Gauss hypergeometric function F 1 2 a,b; c;x  in scaled form.
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 in the Black-Scholes-Merton model
S30BBF
Example Text
Example Data
22 nagf_specfun_opt_lookback_fls_greeks
Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
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
S30NCF
Example Text
Example Data
25 nagf_specfun_opt_heston_term
Heston's model option pricing with term structure
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. 2016