NAG Toolbox

S – approximations of special functions

• S Introduction
• s01ba – ln(1+x)
• nag_specfun_log_shifted
• s01ea – Complex exponential, e^z
• nag_specfun_exp_complex
• s07aa – tanx
• nag_specfun_tan
• s09aa – arcsinx
• nag_specfun_arcsin
• s09ab – arccosx
• nag_specfun_arccos
• s10aa – tanhx
• nag_specfun_tanh
• s10ab – sinhx
• nag_specfun_sinh
• s10ac – coshx
• nag_specfun_cosh
• s11aa – arctanhx
• nag_specfun_arctanh
• s11ab – arcsinhx
• nag_specfun_arcsinh
• s11ac – arccoshx
• nag_specfun_arccosh
• s13aa – Exponential integral E₁(x)
• nag_specfun_integral_exp
• s13ac – Cosine integral Ci(x)
• nag_specfun_integral_cos
• s13ad – Sine integral Si(x)
• nag_specfun_integral_sin
• s14aa – Gamma function
• nag_specfun_gamma
• s14ab – Log gamma function, real argument
• nag_specfun_gamma_log_real
• s14ac – *(x)-lnx where *(x) is the psi function
• nag_specfun_polygamma
• s14ad – Scaled derivatives of ψ(x)
• nag_specfun_polygamma_deriv
• s14ae – Polygamma function ψ⁽ⁿ⁾(x) for real x
• nag_specfun_psi_deriv_real
• s14af – Polygamma function ψ⁽ⁿ⁾(z) for complex z
• nag_specfun_psi_deriv_complex
• s14ag – Logarithm of the gamma function lnΓ(z), complex argument
• nag_specfun_gamma_log_complex
• s14ah – Scaled log gamma function
• nag_specfun_gamma_log_scaled_real
• s14ba – Incomplete gamma functions P(ax) and Q(ax)
• nag_specfun_gamma_incomplete
• s14cb – Logarithm of the beta function lnB(ab)
• nag_specfun_beta_log_real
• s14cc – Incomplete beta function I_x(ab) and its complement 1-I_x
• nag_specfun_beta_incomplete
• s15ab – Cumulative Normal distribution function P(x)
• nag_specfun_cdf_normal
• s15ac – Complement of cumulative Normal distribution function Q(x)
• nag_specfun_compcdf_normal
• s15ad – Complement of error function erfc(x)
• nag_specfun_erfc_real
• s15ae – Error function erf(x)
• nag_specfun_erf_real
• s15af – Dawson's integral
• nag_specfun_dawson
• s15ag – Scaled complement of error function, erfcx(x)
• nag_specfun_erfcx_real
• s15dd – Scaled complex complement of error function, exp(-z²)erfc(-iz)
• nag_specfun_erfc_complex
• s17ac – Bessel function Y₀(x)
• nag_specfun_bessel_y0_real
• s17ad – Bessel function Y₁(x)
• nag_specfun_bessel_y1_real
• s17ae – Bessel function J₀(x)
• nag_specfun_bessel_j0_real
• s17af – Bessel function J₁(x)
• nag_specfun_bessel_j1_real
• s17ag – Airy function Ai(x)
• nag_specfun_airy_ai_real
• s17ah – Airy function Bi(x)
• nag_specfun_airy_bi_real
• s17aj – Airy function Ai'(x)
• nag_specfun_airy_ai_deriv
• s17ak – Airy function Bi'(x)
• nag_specfun_airy_bi_deriv
• s17al – Zeros of Bessel functions J_α(x), J'_α(x), Y_α(x) or Y'_α(x)
• nag_specfun_bessel_zeros
• s17aq – Bessel function vectorized Y₀(x)
• nag_specfun_bessel_y0_real_vector
• s17ar – Bessel function vectorized Y₁(x)
• nag_specfun_bessel_y1_real_vector
• s17as – Bessel function vectorized J₀(x)
• nag_specfun_bessel_j0_real_vector
• s17at – Bessel function vectorized J₁(x)
• nag_specfun_bessel_j1_real_vector
• s17au – Airy function vectorized Ai(x)
• nag_specfun_airy_ai_real_vector
• s17av – Airy function vectorized Bi(x)
• nag_specfun_airy_bi_real_vector
• s17aw – Derivatives of the Airy function, vectorized Ai'(x)
• nag_specfun_airy_ai_deriv_vector
• s17ax – Derivatives of the Airy function, vectorized Bi'(x)
• nag_specfun_airy_bi_deriv_vector
• s17dc – Bessel functions Y_ν+a(z), real a≥0, complex z, ν=0,1,2,…
• nag_specfun_bessel_y_complex
• s17de – Bessel functions J_ν+a(z), real a≥0, complex z, ν=0,1,2,…
• nag_specfun_bessel_j_complex
• s17dg – Airy functions Ai(z) and Ai'(z), complex z
• nag_specfun_airy_ai_complex
• s17dh – Airy functions Bi(z) and Bi'(z), complex z
• nag_specfun_airy_bi_complex
• s17dl – Hankel functions H_ν+a^(j)(z), j=1,2, real a≥0, complex z, ν=0,1,2,…
• nag_specfun_hankel_complex
• s18ac – Modified Bessel function K₀(x)
• nag_specfun_bessel_k0_real
• s18ad – Modified Bessel function K₁(x)
• nag_specfun_bessel_k1_real
• s18ae – Modified Bessel function I₀(x)
• nag_specfun_bessel_i0_real
• s18af – Modified Bessel function I₁(x)
• nag_specfun_bessel_i1_real
• s18aq – Modified Bessel function vectorized K₀(x)
• nag_specfun_bessel_k0_real_vector
• s18ar – Modified Bessel function vectorized K₁(x)
• nag_specfun_bessel_k1_real_vector
• s18as – Modified Bessel function vectorized I₀(x)
• nag_specfun_bessel_i0_real_vector
• s18at – Modified Bessel function vectorized I₁(x)
• nag_specfun_bessel_i1_real_vector
• s18cc – Scaled modified Bessel function e^xK₀(x)
• nag_specfun_bessel_k0_scaled
• s18cd – Scaled modified Bessel function e^xK₁(x)
• nag_specfun_bessel_k1_scaled
• s18ce – Scaled modified Bessel function e^-|x|I₀(x)
• nag_specfun_bessel_i0_scaled
• s18cf – Scaled modified Bessel function e^-|x|I₁(x)
• nag_specfun_bessel_i1_scaled
• s18cq – Scaled modified Bessel function vectorized e^xK₀(x)
• nag_specfun_bessel_k0_scaled_vector
• s18cr – Scaled modified Bessel function vectorized e^xK₁(x)
• nag_specfun_bessel_k1_scaled_vector
• s18cs – Scaled modified Bessel function vectorized e^-|x|I₀(x)
• nag_specfun_bessel_i0_scaled_vector
• s18ct – Scaled modified Bessel function vectorized e^-|x|I₁(x)
• nag_specfun_bessel_i1_scaled_vector
• s18dc – Modified Bessel functions K_ν+a(z), real a≥0, complex z, ν=0,1,2,…
• nag_specfun_bessel_k_complex
• s18de – Modified Bessel functions I_ν+a(z), real a≥0, complex z, ν=0,1,2,…
• nag_specfun_bessel_i_complex
• s18gk – Bessel function of the 1st kind J_α±n(z)
• nag_specfun_bessel_j_seq_complex
• s19aa – Kelvin function berx
• nag_specfun_kelvin_ber
• s19ab – Kelvin function beix
• nag_specfun_kelvin_bei
• s19ac – Kelvin function kerx
• nag_specfun_kelvin_ker
• s19ad – Kelvin function keix
• nag_specfun_kelvin_kei
• s19an – Kelvin function vectorized berx
• nag_specfun_kelvin_ber_vector
• s19ap – Kelvin function vectorized beix
• nag_specfun_kelvin_bei_vector
• s19aq – Kelvin function vectorized kerx
• nag_specfun_kelvin_ker_vector
• s19ar – Kelvin function vectorized keix
• nag_specfun_kelvin_kei_vector
• s20ac – Fresnel integral S(x)
• nag_specfun_fresnel_s
• s20ad – Fresnel integral C(x)
• nag_specfun_fresnel_c
• s20aq – Fresnel integral vectorized S(x)
• nag_specfun_fresnel_s_vector
• s20ar – Fresnel integral vectorized C(x)
• nag_specfun_fresnel_c_vector
• s21ba – Degenerate symmetrised elliptic integral of 1st kind R_C(xy)
• nag_specfun_ellipint_symm_1_degen
• s21bb – Symmetrised elliptic integral of 1st kind R_F(xyz)
• nag_specfun_ellipint_symm_1
• s21bc – Symmetrised elliptic integral of 2nd kind R_D(xyz)
• nag_specfun_ellipint_symm_2
• s21bd – Symmetrised elliptic integral of 3rd kind R_J(xyzr)
• nag_specfun_ellipint_symm_3
• s21be – Elliptic integral of 1st kind, Legendre form, F(ϕ∣m)
• nag_specfun_ellipint_legendre_1
• s21bf – Elliptic integral of 2nd kind, Legendre form, E (ϕ∣m)
• nag_specfun_ellipint_legendre_2
• s21bg – Elliptic integral of 3rd kind, Legendre form, Π (n;ϕ∣m)
• nag_specfun_ellipint_legendre_3
• s21bh – Complete elliptic integral of 1st kind, Legendre form, K (m)
• nag_specfun_ellipint_complete_1
• s21bj – Complete elliptic integral of 2nd kind, Legendre form, E (m)
• nag_specfun_ellipint_complete_2
• s21ca – Jacobian elliptic functions sn, cn and dn of real argument
• nag_specfun_jacellip_real
• s21cb – Jacobian elliptic functions sn, cn and dn of complex argument
• nag_specfun_jacellip_complex
• s21cc – Jacobian theta functions θ_k(xq) of real argument
• nag_specfun_jactheta_real
• s21da – General elliptic integral of 2nd kind F(zk'ab) of complex argument
• nag_specfun_ellipint_general_2
• s22aa – Legendre functions of 1st kind P_n^m(x) or P_n^m(x)
• nag_specfun_legendre_p
• s22ba – Real confluent hypergeometric function ₁F₁ (abx)
• nag_specfun_1f1_real
• s22bb – Real confluent hypergeometric function ₁F₁ (abx) in scaled form
• nag_specfun_1f1_real_scaled
• s22be – Real Gauss hypergeometric function ₂F₁ (a,bcx)
• nag_specfun_2f1_real
• s22bf – Real Gauss hypergeometric function ₂F₁ (a,b;c;x) in scaled form.
• nag_specfun_2f1_real_scaled
• s30aa – Black–Scholes–Merton option pricing formula
• nag_specfun_opt_bsm_price
• s30ab – Black–Scholes–Merton option pricing formula with Greeks
• nag_specfun_opt_bsm_greeks
• s30ba – Floating-strike lookback option pricing formula in the Black-Scholes-Merton model
• nag_specfun_opt_lookback_fls_price
• s30bb – Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model
• nag_specfun_opt_lookback_fls_greeks
• s30ca – Binary option, cash-or-nothing pricing formula
• nag_specfun_opt_binary_con_price
• s30cb – Binary option, cash-or-nothing pricing formula with Greeks
• nag_specfun_opt_binary_con_greeks
• s30cc – Binary option, asset-or-nothing pricing formula
• nag_specfun_opt_binary_aon_price
• s30cd – Binary option, asset-or-nothing pricing formula with Greeks
• nag_specfun_opt_binary_aon_greeks
• s30fa – Standard barrier option pricing formula
• nag_specfun_opt_barrier_std_price
• s30ja – Jump-diffusion, Merton's model, option pricing formula
• nag_specfun_opt_jumpdiff_merton_price
• s30jb – Jump-diffusion, Merton's model, option pricing formula with Greeks
• nag_specfun_opt_jumpdiff_merton_greeks
• s30na – Heston's model option pricing formula
• nag_specfun_opt_heston_price
• s30nb – Heston's model option pricing formula with Greeks
• nag_specfun_opt_heston_greeks
• s30nc – Heston's model option pricing with term structure
• nag_specfun_opt_heston_term
• s30qc – American option, Bjerksund and Stensland pricing formula
• nag_specfun_opt_amer_bs_price
• s30sa – Asian option, geometric continuous average rate pricing formula
• nag_specfun_opt_asian_geom_price
• s30sb – Asian option, geometric continuous average rate pricing formula with Greeks
• nag_specfun_opt_asian_geom_greeks

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