S Chapter Contents : NAG Library Manual, Mark 23

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, e^z
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 J_α(x), J_α^′(x), Y_α(x) or Y_α^′(x)
S17DCF Example Text Example Data	13	nagf_specfun_bessel_y_complex Bessel functions Y_{ν + a}(z), real a ≥ 0, complex z, ν = 0,1,2, …
S17DEF Example Text Example Data	13	nagf_specfun_bessel_j_complex Bessel functions J_{ν + a}(z), real a ≥ 0, 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 H_{ν + a}^(j)(z), j = 1,2, real a ≥ 0, 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 e^xK₀(x)
S18CDF Example Text Example Data	10	nagf_specfun_bessel_k1_scaled Scaled modified Bessel function e^xK₁(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 K_{ν + a}(z), real a ≥ 0, complex z, ν = 0,1,2, …
S18DEF Example Text Example Data	13	nagf_specfun_bessel_i_complex Modified Bessel functions I_{ν + a}(z), real a ≥ 0, complex z, ν = 0,1,2, …
S18GKF Example Text Example Data	21	nagf_specfun_bessel_j_seq_complex Bessel function of the 1st kind J_{α ± 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 R_C(x,y)
S21BBF Example Text	8	nagf_specfun_ellipint_symm_1 Symmetrised elliptic integral of 1st kind R_F(x,y,z)
S21BCF Example Text	8	nagf_specfun_ellipint_symm_2 Symmetrised elliptic integral of 2nd kind R_D(x,y,z)
S21BDF Example Text	8	nagf_specfun_elliptic_symm_3 Symmetrised elliptic integral of 3rd kind R_J(x,y,z,r)
S21BEF Example Text	22	nagf_specfun_ellipint_legendre_1 Elliptic integral of 1st kind, Legendre form, F(φ ∣ m)
S21BFF Example Text	22	nagf_specfun_ellipint_legendre_2 Elliptic integral of 2nd kind, Legendre form, E (φ ∣ m)
S21BGF Example Text	22	nagf_specfun_ellipint_legendre_3 Elliptic integral of 3rd kind, Legendre form, Π (n ; φ ∣ m)
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 θ_k(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 P_n^m(x) or P_n^m(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

NAG Library Chapter Contents

S – Approximations of Special Functions

S Chapter Introduction

NAG Library Chapter ContentsS – Approximations of Special Functions

S Chapter Introduction

NAG Library Chapter Contents

S – Approximations of Special Functions