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 |
2 |
nagf_specfun_integral_cos
Cosine integral Cix |
S13ADF
Example Text
Example Data |
5 |
nagf_specfun_integral_sin
Sine integral Six |
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
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 |
23 |
nagf_specfun_gamma_log_scaled_real
Scaled log gamma function |
S14BAF
Example Text
Example Data |
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 lnB,a,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 |
1 |
nagf_specfun_bessel_y0_real
Bessel function Y0x |
S17ADF
Example Text
Example Data |
1 |
nagf_specfun_bessel_y1_real
Bessel function Y1x |
S17AEF
Example Text
Example Data |
5 |
nagf_specfun_bessel_j0_real
Bessel function J0x |
S17AFF
Example Text
Example Data |
5 |
nagf_specfun_bessel_j1_real
Bessel function J1x |
S17AGF
Example Text
Example Data |
8 |
nagf_specfun_airy_ai_real
Airy function Aix |
S17AHF
Example Text
Example Data |
8 |
nagf_specfun_airy_bi_real
Airy function Bix |
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 Jαx, Jα′x, Yαx or Yα′x |
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
Airy function vectorized Ai′x |
S17AXF
Example Text
Example Data |
24 |
nagf_specfun_airy_bi_deriv_vector
Airy function vectorized Bi′x |
S17DCF
Example Text
Example Data |
13 |
nagf_specfun_bessel_y_complex
Bessel functions Yν+az, real a≥0, complex z, ν=0,1,2,… |
S17DEF
Example Text
Example Data |
13 |
nagf_specfun_bessel_j_complex
Bessel functions Jν+az, real a≥0, complex z, ν=0,1,2,… |
S17DGF
Example Text
Example Data |
13 |
nagf_specfun_airy_ai_complex
Airy functions Aiz and Ai′z, complex z |
S17DHF
Example Text
Example Data |
13 |
nagf_specfun_airy_bi_complex
Airy functions Biz and Bi′z, complex z |
S17DLF
Example Text
Example Data |
13 |
nagf_specfun_hankel_complex
Hankel functions Hν+ajz, 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 K0x |
S18ADF
Example Text
Example Data |
1 |
nagf_specfun_bessel_k1_real
Modified Bessel function K1x |
S18AEF
Example Text
Example Data |
5 |
nagf_specfun_bessel_i0_real
Modified Bessel function I0x |
S18AFF
Example Text
Example Data |
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 a≥0, complex z, ν=0,1,2,… |
S18DEF
Example Text
Example Data |
13 |
nagf_specfun_bessel_i_complex
Modified Bessel functions Iν+az, 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 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 |
5 |
nagf_specfun_fresnel_s
Fresnel integral Sx |
S20ADF
Example Text
Example Data |
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 |
22 |
nagf_specfun_ellipint_legendre_1
Elliptic integral of 1st kind, Legendre form, Fϕ∣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 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
Example Data |
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 |
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 |