S Chapter Contents

S Introduction

s01ba – ln((1+x))

nag_specfun_log_shifted – s01ba

s01ea – Complex exponential, e^z

nag_specfun_exp_complex – s01ea

s07aa – tan(x)

nag_specfun_tan – s07aa

s09aa – arcsin(x)

nag_specfun_arcsin – s09aa

s09ab – arccos(x)

nag_specfun_arccos – s09ab

s10aa – tanh(x)

nag_specfun_tanh – s10aa

s10ab – sinh(x)

nag_specfun_sinh – s10ab

s10ac – cosh(x)

nag_specfun_cosh – s10ac

s11aa – arctanh(x)

nag_specfun_arctanh – s11aa

s11ab – arcsinh(x)

nag_specfun_arcsinh – s11ab

s11ac – arccosh(x)

nag_specfun_arccosh – s11ac

s13aa – Exponential integral E_1(x)

nag_specfun_integral_exp – s13aa

s13ac – Cosine integral Ci((x))

nag_specfun_integral_cos – s13ac

s13ad – Sine integral Si((x))

nag_specfun_integral_sin – s13ad

s14aa – Gamma function

nag_specfun_gamma – s14aa

s14ab – Log gamma function, real argument

nag_specfun_gamma_log_real – s14ab

s14ac – psi (x)-ln(x)

nag_specfun_polygamma – s14ac

s14ad – Scaled derivatives of psi (x)

nag_specfun_polygamma_deriv – s14ad

s14ae – Polygamma function psi ^(n)(x) for real x

nag_specfun_psi_deriv_real – s14ae

s14af – Polygamma function psi ^(n)(z) for complex z

nag_specfun_psi_deriv_complex – s14af

s14ag – Logarithm of the gamma function ln( Gamma )(z), complex argument

nag_specfun_gamma_log_complex – s14ag

s14ah – Scaled log gamma function

nag_specfun_gamma_log_scaled_real – s14ah

s14ba – Incomplete gamma functions P(ax) and Q(ax)

nag_specfun_gamma_incomplete – s14ba

s15ab – Cumulative Normal distribution function P(x)

nag_specfun_cdf_normal – s15ab

s15ac – Complement of cumulative Normal distribution function Q(x)

nag_specfun_compcdf_normal – s15ac

s15ad – Complement of error function erfc((x))

nag_specfun_erfc_real – s15ad

s15ae – Error function erf((x))

nag_specfun_erf_real – s15ae

s15af – Dawson's integral

nag_specfun_dawson – s15af

s15ag – Scaled complement of error function, erfcx((x))

nag_specfun_erfcx_real – s15ag

s15dd – Scaled complex complement of error function, exp((-z^2))erfc((-iz))

nag_specfun_erfc_complex – s15dd

s17ac – Bessel function Y_0(x)

nag_specfun_bessel_y0_real – s17ac

s17ad – Bessel function Y_1(x)

nag_specfun_bessel_y1_real – s17ad

s17ae – Bessel function J_0(x)

nag_specfun_bessel_j0_real – s17ae

s17af – Bessel function J_1(x)

nag_specfun_bessel_j1_real – s17af

s17ag – Airy function Ai((x))

nag_specfun_airy_ai_real – s17ag

s17ah – Airy function Bi((x))

nag_specfun_airy_bi_real – s17ah

s17aj – Airy function Ai'((x))

nag_specfun_airy_ai_deriv – s17aj

s17ak – Airy function Bi'((x))

nag_specfun_airy_bi_deriv – s17ak

s17al – Zeros of Bessel functions J_ alpha (x), J'_ alpha (x), Y_ alpha (x) or Y'_ alpha (x)

nag_specfun_bessel_zeros – s17al

s17aq – Bessel function vectorized Y_0(x)

nag_specfun_bessel_y0_real_vector – s17aq

s17ar – Bessel function vectorized Y_1(x)

nag_specfun_bessel_y1_real_vector – s17ar

s17as – Bessel function vectorized J_0(x)

nag_specfun_bessel_j0_real_vector – s17as

s17at – Bessel function vectorized J_1(x)

nag_specfun_bessel_j1_real_vector – s17at

s17au – Airy function vectorized Ai((x))

nag_specfun_airy_ai_real_vector – s17au

s17av – Airy function vectorized Bi((x))

nag_specfun_airy_bi_real_vector – s17av

s17aw – Airy function vectorized Ai'((x))

nag_specfun_airy_ai_deriv_vector – s17aw

s17ax – Airy function vectorized Bi'((x))

nag_specfun_airy_bi_deriv_vector – s17ax

s17dc – Bessel functions Y_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

nag_specfun_bessel_y_complex – s17dc

s17de – Bessel functions J_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

nag_specfun_bessel_j_complex – s17de

s17dg – Airy functions Ai((z)) and Ai'((z)), complex z

nag_specfun_airy_ai_complex – s17dg

s17dh – Airy functions Bi((z)) and Bi'((z)), complex z

nag_specfun_airy_bi_complex – s17dh

s17dl – Hankel functions H_ nu +a^(j)(z), j=1,2, real a >= 0, complex z, nu =0,1,2, ...

nag_specfun_hankel_complex – s17dl

s18ac – Modified Bessel function K_0(x)

nag_specfun_bessel_k0_real – s18ac

s18ad – Modified Bessel function K_1(x)

nag_specfun_bessel_k1_real – s18ad

s18ae – Modified Bessel function I_0(x)

nag_specfun_bessel_i0_real – s18ae

s18af – Modified Bessel function I_1(x)

nag_specfun_bessel_i1_real – s18af

s18aq – Modified Bessel function vectorized K_0(x)

nag_specfun_bessel_k0_real_vector – s18aq

s18ar – Modified Bessel function vectorized K_1(x)

nag_specfun_bessel_k1_real_vector – s18ar

s18as – Modified Bessel function vectorized I_0(x)

nag_specfun_bessel_i0_real_vector – s18as

s18at – Modified Bessel function vectorized I_1(x)

nag_specfun_bessel_i1_real_vector – s18at

s18cc – Scaled modified Bessel function e^xK_0(x)

nag_specfun_bessel_k0_scaled – s18cc

s18cd – Scaled modified Bessel function e^xK_1(x)

nag_specfun_bessel_k1_scaled – s18cd

s18ce – Scaled modified Bessel function e^-|x|I_0(x)

nag_specfun_bessel_i0_scaled – s18ce

s18cf – Scaled modified Bessel function e^-|x|I_1(x)

nag_specfun_bessel_i1_scaled – s18cf

s18cq – Scaled modified Bessel function vectorized e^xK_0(x)

nag_specfun_bessel_k0_scaled_vector – s18cq

s18cr – Scaled modified Bessel function vectorized e^xK_1(x)

nag_specfun_bessel_k1_scaled_vector – s18cr

s18cs – Scaled modified Bessel function vectorized e^-|x|I_0(x)

nag_specfun_bessel_i0_scaled_vector – s18cs

s18ct – Scaled modified Bessel function vectorized e^-|x|I_1(x)

nag_specfun_bessel_i1_scaled_vector – s18ct

s18dc – Modified Bessel functions K_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

nag_specfun_bessel_k_complex – s18dc

s18de – Modified Bessel functions I_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

nag_specfun_bessel_i_complex – s18de

s18gk – Bessel function of the 1st kind J_ alpha ±n(z)

nag_specfun_bessel_j_seq_complex – s18gk

s19aa – Kelvin function ber(x)

nag_specfun_kelvin_ber – s19aa

s19ab – Kelvin function bei(x)

nag_specfun_kelvin_bei – s19ab

s19ac – Kelvin function ker(x)

nag_specfun_kelvin_ker – s19ac

s19ad – Kelvin function kei(x)

nag_specfun_kelvin_kei – s19ad

s19an – Kelvin function vectorized ber(x)

nag_specfun_kelvin_ber_vector – s19an

s19ap – Kelvin function vectorized bei(x)

nag_specfun_kelvin_bei_vector – s19ap

s19aq – Kelvin function vectorized ker(x)

nag_specfun_kelvin_ker_vector – s19aq

s19ar – Kelvin function vectorized kei(x)

nag_specfun_kelvin_kei_vector – s19ar

s20ac – Fresnel integral S(x)

nag_specfun_fresnel_s – s20ac

s20ad – Fresnel integral C(x)

nag_specfun_fresnel_c – s20ad

s20aq – Fresnel integral vectorized S(x)

nag_specfun_fresnel_s_vector – s20aq

s20ar – Fresnel integral vectorized C(x)

nag_specfun_fresnel_c_vector – s20ar

s21ba – Degenerate symmetrised elliptic integral of 1st kind R_C(xy)

nag_specfun_ellipint_symm_1_degen – s21ba

s21bb – Symmetrised elliptic integral of 1st kind R_F(xyz)

nag_specfun_ellipint_symm_1 – s21bb

s21bc – Symmetrised elliptic integral of 2nd kind R_D(xyz)

nag_specfun_ellipint_symm_2 – s21bc

s21bd – Symmetrised elliptic integral of 3rd kind R_J(xyzr)

nag_specfun_ellipint_symm_3 – s21bd

s21be – Elliptic integral of 1st kind, Legendre form, F( phi | m)

nag_specfun_ellipint_legendre_1 – s21be

s21bf – Elliptic integral of 2nd kind, Legendre form, E ( phi | m)

nag_specfun_ellipint_legendre_2 – s21bf

s21bg – Elliptic integral of 3rd kind, Legendre form, Pi (n; phi | m)

nag_specfun_ellipint_legendre_3 – s21bg

s21bh – Complete elliptic integral of 1st kind, Legendre form, K (m)

nag_specfun_ellipint_complete_1 – s21bh

s21bj – Complete elliptic integral of 2nd kind, Legendre form, E (m)

nag_specfun_ellipint_complete_2 – s21bj

s21ca – Jacobian elliptic functions sn, cn and dn of real argument

nag_specfun_jacellip_real – s21ca

s21cb – Jacobian elliptic functions sn, cn and dn of complex argument

nag_specfun_jacellip_complex – s21cb

s21cc – Jacobian theta functions theta _k(xq) of real argument

nag_specfun_jactheta_real – s21cc

s21da – General elliptic integral of 2nd kind F(zk'ab) of complex argument

nag_specfun_ellipint_general_2 – s21da

s22aa – Legendre functions of 1st kind P_n^m(x) or (P_n^m)^-(x)

nag_specfun_legendre_p – s22aa

s30aa – Black–Scholes–Merton option pricing formula

nag_specfun_opt_bsm_price – s30aa

s30ab – Black–Scholes–Merton option pricing formula with Greeks

nag_specfun_opt_bsm_greeks – s30ab

s30ba – Floating-strike lookback option pricing formula

nag_specfun_opt_lookback_fls_price – s30ba

s30bb – Floating-strike lookback option pricing formula with Greeks

nag_specfun_opt_lookback_fls_greeks – s30bb

s30ca – Binary option: cash-or-nothing pricing formula

nag_specfun_opt_binary_con_price – s30ca

s30cb – Binary option: cash-or-nothing pricing formula with Greeks

nag_specfun_opt_binary_con_greeks – s30cb

s30cc – Binary option: asset-or-nothing pricing formula

nag_specfun_opt_binary_aon_price – s30cc

s30cd – Binary option: asset-or-nothing pricing formula with Greeks

nag_specfun_opt_binary_aon_greeks – s30cd

s30fa – Standard barrier option pricing formula

nag_specfun_opt_barrier_std_price – s30fa

s30ja – Jump-diffusion, Merton's model, option pricing formula

nag_specfun_opt_jumpdiff_merton_price – s30ja

s30jb – Jump-diffusion, Merton's model, option pricing formula with Greeks

nag_specfun_opt_jumpdiff_merton_greeks – s30jb

s30na – Heston's model option pricing formula

nag_specfun_opt_heston_price – s30na

s30nb – Heston's model option pricing formula with Greeks

nag_specfun_opt_heston_greeks – s30nb

s30qc – American option: Bjerksund and Stensland pricing formula

nag_specfun_opt_amer_bs_price – s30qc

s30sa – Asian option: geometric continuous average rate pricing formula

nag_specfun_opt_asian_geom_price – s30sa

s30sb – Asian option: geometric continuous average rate pricing formula with Greeks

nag_specfun_opt_asian_geom_greeks – s30sb

S – Approximations of Special Functions