| Function Name |
Mark of Introduction |
Purpose |
| s01bac
Example Text Example Data |
7 | nag_shifted_log ln(1 + x) |
| s10aac
Example Text Example Data |
1 | nag_tanh Hyperbolic tangent, tanh x |
| s10abc
Example Text Example Data |
1 | nag_sinh Hyperbolic sine, sinh x |
| s10acc
Example Text Example Data |
1 | nag_cosh Hyperbolic cosine, cosh x |
| s11aac
Example Text Example Data |
1 | nag_arctanh Inverse hyperbolic tangent, arctanh x |
| s11abc
Example Text Example Data |
1 | nag_arcsinh Inverse hyperbolic sine, arcsinh x |
| s11acc
Example Text Example Data |
1 | nag_arccosh Inverse hyperbolic cosine, arccosh x |
| s13aac
Example Text Example Data Example Plot |
1 | nag_exp_integral Exponential integral E1(x) |
| s13acc
Example Text Example Data Example Plot |
1 | nag_cos_integral Cosine integral Ci(x) |
| s13adc
Example Text Example Data Example Plot |
1 | nag_sin_integral Sine integral Si(x) |
| s14aac
Example Text Example Data Example Plot |
1 | nag_gamma Gamma function Γ(x) |
| s14abc
Example Text Example Data Example Plot |
1 | nag_log_gamma Log gamma function ln(Γ(x)) |
| s14acc
Example Text Example Data Example Plot |
7 | nag_polygamma_fun *(x) − lnx where *(x) is the psi function |
| s14adc
Example Text Example Data |
7 | nag_polygamma_deriv Scaled derivatives of ψ(x) |
| s14aec
Example Text Example Data |
6 | nag_real_polygamma Derivative of the psi function ψ(x) |
| s14afc
Example Text Example Data |
6 | nag_complex_polygamma Derivative of the psi function ψ(z) |
| s14agc
Example Text Example Data |
7 | nag_complex_log_gamma Logarithm of the gamma function lnΓ(z), complex argument |
| s14ahc
Example Text Example Data Example Plot |
9 | nag_scaled_log_gamma Scaled log gamma function lnG(x), where G(x) = Γ(x + 1) / (x / e)x |
| s14bac
Example Text Example Data Example Plot |
1 | nag_incomplete_gamma Incomplete gamma functions P(a,x) and Q(a,x) |
| s14cbc
Example Text Example Data |
23 | nag_log_beta Logarithm of the beta function lnB(a,b) |
| s14ccc
Example Text Example Data |
23 | nag_incomplete_beta Incomplete beta function Ix(a,b) and its complement 1 − Ix |
| s15abc
Example Text Example Data |
1 | nag_cumul_normal Cumulative Normal distribution function P(x) |
| s15acc
Example Text Example Data |
1 | nag_cumul_normal_complem Complement of cumulative Normal distribution function Q(x) |
| s15adc
Example Text Example Data |
1 | nag_erfc Complement of error function erfc(x) |
| s15aec
Example Text Example Data |
1 | nag_erf Error function erf(x) |
| s15afc
Example Text Example Data |
7 | nag_dawson Dawson's integral |
| s15agc
Example Text Example Data |
9 | nag_erfcx Scaled complement of error function, erfcx(x) |
| s15ddc
Example Text Example Data |
7 | nag_complex_erfc Scaled complex complement of error function, exp( − z2)erfc( − iz) |
| s17acc
Example Text Example Data Example Plot |
1 | nag_bessel_y0 Bessel function Y0(x) |
| s17adc
Example Text Example Data Example Plot |
1 | nag_bessel_y1 Bessel function Y1(x) |
| s17aec
Example Text Example Data Example Plot |
1 | nag_bessel_j0 Bessel function J0(x) |
| s17afc
Example Text Example Data Example Plot |
1 | nag_bessel_j1 Bessel function J1(x) |
| s17agc
Example Text Example Data Example Plot |
1 | nag_airy_ai Airy function Ai(x) |
| s17ahc
Example Text Example Data Example Plot |
1 | nag_airy_bi Airy function Bi(x) |
| s17ajc
Example Text Example Data Example Plot |
1 | nag_airy_ai_deriv Airy function Ai′(x) |
| s17akc
Example Text Example Data Example Plot |
1 | nag_airy_bi_deriv Airy function Bi′(x) |
| s17alc
Example Text Example Data |
6 | nag_bessel_zeros Zeros of Bessel functions Jα(x), Jα ′ (x), Yα(x) or Yα ′ (x) |
| s17aqc
Example Text Example Data |
23 | nag_bessel_y0_vector Bessel function vectorized Y0(x) |
| s17arc
Example Text Example Data |
23 | nag_bessel_y1_vector Bessel function vectorized Y1(x) |
| s17asc
Example Text Example Data |
23 | nag_bessel_j0_vector Bessel function vectorized J0(x) |
| s17atc
Example Text Example Data |
23 | nag_bessel_j1_vector Bessel function vectorized J1(x) |
| s17auc
Example Text Example Data |
23 | nag_airy_ai_vector Airy function vectorized Ai(x) |
| s17avc
Example Text Example Data |
23 | nag_airy_bi_vector Airy function vectorized Bi(x) |
| s17awc
Example Text Example Data |
23 | nag_airy_ai_deriv_vector Derivatives of the Airy function, vectorized Ai′(x) |
| s17axc
Example Text Example Data |
23 | nag_airy_bi_deriv_vector Derivatives of the Airy function, vectorized Bi′(x) |
| s17dcc
Example Text Example Data |
7 | nag_complex_bessel_y Bessel functions Yν + a(z), real a ≥ 0, complex z, ν = 0,1,2, … |
| s17dec
Example Text Example Data |
7 | nag_complex_bessel_j Bessel functions Jν + a(z), real a ≥ 0, complex z, ν = 0,1,2, … |
| s17dgc
Example Text Example Data |
7 | nag_complex_airy_ai Airy functions Ai(z) and Ai′(z), complex z |
| s17dhc
Example Text Example Data |
7 | nag_complex_airy_bi Airy functions Bi(z) and Bi′(z), complex z |
| s17dlc
Example Text Example Data |
7 | nag_complex_hankel Hankel functions Hν + a(j)(z), j = 1,2, real a ≥ 0, complex z, ν=0,1,2, … |
| s18acc
Example Text Example Data Example Plot |
1 | nag_bessel_k0 Modified Bessel function K0(x) |
| s18adc
Example Text Example Data Example Plot |
1 | nag_bessel_k1 Modified Bessel function K1(x) |
| s18aec
Example Text Example Data Example Plot |
1 | nag_bessel_i0 Modified Bessel function I0(x) |
| s18afc
Example Text Example Data Example Plot |
1 | nag_bessel_i1 Modified Bessel function I1(x) |
| s18aqc
Example Text Example Data |
23 | nag_bessel_k0_vector Modified Bessel function vectorized K0(x) |
| s18arc
Example Text Example Data |
23 | nag_bessel_k1_vector Modified Bessel function vectorized K1(x) |
| s18asc
Example Text Example Data |
23 | nag_bessel_i0_vector Modified Bessel function vectorized I0(x) |
| s18atc
Example Text Example Data |
23 | nag_bessel_i1_vector Modified Bessel function vectorized I1(x) |
| s18ccc
Example Text Example Data |
2 | nag_bessel_k0_scaled Scaled modified Bessel function exK0(x) |
| s18cdc
Example Text Example Data |
2 | nag_bessel_k1_scaled Scaled modified Bessel function exK1(x) |
| s18cec
Example Text Example Data |
2 | nag_bessel_i0_scaled Scaled modified Bessel function e − |x|I0(x) |
| s18cfc
Example Text Example Data |
2 | nag_bessel_i1_scaled Scaled modified Bessel function e − |x|I1(x) |
| s18cqc
Example Text Example Data |
23 | nag_bessel_k0_scaled_vector Scaled modified Bessel function vectorized exK0(x) |
| s18crc
Example Text Example Data |
23 | nag_bessel_k1_scaled_vector Scaled modified Bessel function vectorized exK1(x) |
| s18csc
Example Text Example Data |
23 | nag_bessel_i0_scaled_vector Scaled modified Bessel function vectorized e − |x|I0(x) |
| s18ctc
Example Text Example Data |
23 | nag_bessel_i1_scaled_vector Scaled modified Bessel function vectorized e − |x|I1(x) |
| s18dcc
Example Text Example Data |
7 | nag_complex_bessel_k Modified Bessel functions Kν + a(z), real a ≥ 0, complex z, ν = 0,1,2, … |
| s18dec
Example Text Example Data |
7 | nag_complex_bessel_i Modified Bessel functions Iν + a(z), real a ≥ 0, complex z, ν = 0,1,2, … |
| s18ecc
Example Text Example Data |
6 | nag_bessel_i_nu_scaled Scaled modified Bessel function e − x Iν / 4(x) |
| s18edc
Example Text Example Data |
6 | nag_bessel_k_nu_scaled Scaled modified Bessel function exKν / 4(x) |
| s18eec
Example Text Example Data |
6 | nag_bessel_i_nu Modified Bessel function Iν / 4(x) |
| s18efc
Example Text Example Data |
6 | nag_bessel_k_nu Modified Bessel function Kν / 4(x) |
| s18egc
Example Text Example Data |
6 | nag_bessel_k_alpha Modified Bessel functions Kα + n(x) for real x > 0, selected values of α ≥ 0 and n = 0,1, … ,N |
| s18ehc
Example Text Example Data |
6 | nag_bessel_k_alpha_scaled Scaled modified Bessel functions exKα + n(x) for real x > 0, selected values of α ≥ 0 and n = 0,1, … ,N |
| s18ejc
Example Text Example Data |
6 | nag_bessel_i_alpha Modified Bessel functions Iα + n − 1(x) or Iα − n + 1(x) for real x ≠ 0, non-negative α < 1 and n = 1,2, … ,|N| + 1 |
| s18ekc
Example Text Example Data |
6 | nag_bessel_j_alpha Bessel functions Jα + n − 1(x) or Jα − n + 1(x) for real x ≠ 0, non-negative α < 1 and n = 1,2, … ,|N| + 1 |
| s18gkc
Example Text Example Data |
7 | nag_complex_bessel_j_seq Bessel function of the 1st kind Jα ± n(z) |
| s19aac
Example Text Example Data |
1 | nag_kelvin_ber Kelvin function berx |
| s19abc
Example Text Example Data |
1 | nag_kelvin_bei Kelvin function beix |
| s19acc
Example Text Example Data |
1 | nag_kelvin_ker Kelvin function kerx |
| s19adc
Example Text Example Data |
1 | nag_kelvin_kei Kelvin function keix |
| s19anc
Example Text Example Data |
23 | nag_kelvin_ber_vector Kelvin function vectorized berx |
| s19apc
Example Text Example Data |
23 | nag_kelvin_bei_vector Kelvin function vectorized beix |
| s19aqc
Example Text Example Data |
23 | nag_kelvin_ker_vector Kelvin function vectorized kerx |
| s19arc
Example Text Example Data |
23 | nag_kelvin_kei_vector Kelvin function vectorized keix |
| s20acc
Example Text Example Data Example Plot |
1 | nag_fresnel_s Fresnel integral S(x) |
| s20adc
Example Text Example Data Example Plot |
1 | nag_fresnel_c Fresnel integral C(x) |
| s20aqc
Example Text Example Data |
23 | nag_fresnel_s_vector Fresnel integral vectorized S(x) |
| s20arc
Example Text Example Data |
23 | nag_fresnel_c_vector Fresnel integral vectorized C(x) |
| s21bac
Example Text |
1 | nag_elliptic_integral_rc Degenerate symmetrised elliptic integral of 1st kind RC(x,y) |
| s21bbc
Example Text |
1 | nag_elliptic_integral_rf Symmetrised elliptic integral of 1st kind RF(x,y,z) |
| s21bcc
Example Text |
1 | nag_elliptic_integral_rd Symmetrised elliptic integral of 2nd kind RD(x,y,z) |
| s21bdc
Example Text |
1 | nag_elliptic_integral_rj Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r) |
| s21bec
Example Text |
9 | nag_elliptic_integral_F Elliptic integral of 1st kind, Legendre form, F(φ ∣ m) |
| s21bfc
Example Text |
9 | nag_elliptic_integral_E Elliptic integral of 2nd kind, Legendre form, E (φ ∣ m) |
| s21bgc
Example Text |
9 | nag_elliptic_integral_pi Elliptic integral of 3rd kind, Legendre form, Π (n ; φ ∣ m) |
| s21bhc
Example Text |
9 | nag_elliptic_integral_complete_K Complete elliptic integral of 1st kind, Legendre form, K (m) |
| s21bjc
Example Text |
9 | nag_elliptic_integral_complete_E Complete elliptic integral of 2nd kind, Legendre form, E (m) |
| s21cac
Example Text Example Data |
7 | nag_real_jacobian_elliptic Jacobian elliptic functions sn, cn and dn of real argument |
| s21cbc
Example Text Example Data |
6 | nag_jacobian_elliptic Jacobian elliptic functions sn, cn and dn of complex argument |
| s21ccc
Example Text Example Data |
6 | nag_jacobian_theta Jacobian theta functions with real arguments |
| s21dac
Example Text Example Data |
6 | nag_general_elliptic_integral_f Elliptic integrals of the second kind with complex arguments |
| s22aac
Example Text Example Data |
6 | nag_legendre_p Legendre and associated Legendre functions of the first kind with real arguments |
| s22bac
Example Text |
24 | nag_specfun_1f1_real Real confluent hypergeometric function 1F1 (a ; b ; x) |
| s22bbc
Example Text |
24 | nag_specfun_1f1_real_scaled Real confluent hypergeometric function 1F1 (a ; b ; x) in scaled form |
| s22bec
Example Text |
24 | nag_specfun_2f1_real Real Gauss hypergeometric function 2F1 (a,b ; c ; x) |
| s22bfc
Example Text |
24 | nag_specfun_2f1_real_scaled Real Gauss hypergeometric function 2F1 (a,b ; c ; x) in scaled form. |
| s30aac
Example Text Example Data |
9 | nag_bsm_price Black–Scholes–Merton option pricing formula |
| s30abc
Example Text Example Data |
9 | nag_bsm_greeks Black–Scholes–Merton option pricing formula with Greeks |
| s30bac
Example Text Example Data |
9 | nag_lookback_fls_price Floating-strike lookback option pricing formula in the Black-Scholes-Merton model |
| s30bbc
Example Text Example Data |
9 | nag_lookback_fls_greeks Floating-strike lookback option pricing formula with Greeks in the Black-Scholes-Merton model |
| s30cac
Example Text Example Data |
9 | nag_binary_con_price Binary option, cash-or-nothing pricing formula |
| s30cbc
Example Text Example Data |
9 | nag_binary_con_greeks Binary option, cash-or-nothing pricing formula with Greeks |
| s30ccc
Example Text Example Data |
9 | nag_binary_aon_price Binary option, asset-or-nothing pricing formula |
| s30cdc
Example Text Example Data |
9 | nag_binary_aon_greeks Binary option, asset-or-nothing pricing formula with Greeks |
| s30fac
Example Text Example Data |
9 | nag_barrier_std_price Standard barrier option pricing formula |
| s30jac
Example Text Example Data |
9 | nag_jumpdiff_merton_price Jump-diffusion, Merton's model, option pricing formula |
| s30jbc
Example Text Example Data |
9 | nag_jumpdiff_merton_greeks Jump-diffusion, Merton's model, option pricing formula with Greeks |
| s30nac
Example Text Example Data |
9 | nag_heston_price Heston's model option pricing formula |
| s30nbc
Example Text Example Data |
23 | nag_heston_greeks Heston's model option pricing formula with Greeks |
| s30ncc
Example Text Example Data |
24 | nag_heston_term Heston's model option pricing with term structure |
| s30qcc
Example Text Example Data |
9 | nag_amer_bs_price American option, Bjerksund and Stensland pricing formula |
| s30sac
Example Text Example Data |
9 | nag_asian_geom_price Asian option, geometric continuous average rate pricing formula |
| s30sbc
Example Text Example Data |
9 | nag_asian_geom_greeks Asian option, geometric continuous average rate pricing formula with Greeks |