|
Routine Name |
Mark of Introduction |
Purpose |
| s01bac | 7 |
nag_shifted_log
ln (1+x) |
| s10aac | 1 |
nag_tanh
Hyperbolic tangent, tanh x |
| s10abc | 1 |
nag_sinh
Hyperbolic sine, sinh x |
| s10acc | 1 |
nag_cosh
Hyperbolic cosine, cosh x |
| s11aac | 1 |
nag_arctanh
Inverse hyperbolic tangent, arctanh x |
| s11abc | 1 |
nag_arcsinh
Inverse hyperbolic sine, arcsinh x |
| s11acc | 1 |
nag_arccosh
Inverse hyperbolic cosine, arccosh x |
| s13aac | 1 |
nag_exp_integral
Exponential integral E1 (x) |
| s13acc | 1 |
nag_cos_integral
Cosine integral Ci(x) |
| s13adc | 1 |
nag_sin_integral
Sine integral Si(x) |
| s14aac | 1 |
nag_gamma
Gamma function Γ (x) |
| s14abc | 1 |
nag_log_gamma
Log Gamma function ln(Γ (x)) |
| s14acc | 7 |
nag_polygamma_fun
ψ (x) - ln x |
| s14adc | 7 |
nag_polygamma_deriv
Scaled derivatives of ψ (x) |
| s14aec | 6 |
nag_real_polygamma
Derivative of the psi function ψ (x) |
| s14afc | 6 |
nag_complex_polygamma
Derivative of the psi function ψ (z) |
| s14agc | 7 |
nag_complex_log_gamma
Logarithm of the Gamma function ln Γ (z) |
| s14bac | 1 |
nag_incomplete_gamma
Incomplete Gamma functions P(a,x) and Q(a,x) |
| s15abc | 1 |
nag_cumul_normal
Cumulative Normal distribution function P(x) |
| s15acc | 1 |
nag_cumul_normal_complem
Complement of cumulative Normal distribution function Q(x) |
| s15adc | 1 |
nag_erfc
Complement of error function erfc(x) |
| s15aec | 1 |
nag_erf
Error function erf(x) |
| s15afc | 7 |
nag_dawson
Dawson's integral |
| s15ddc | 7 |
nag_complex_erfc
Scaled complex complement of error function, exp(-z2) erfc(-iz) |
| s17acc | 1 |
nag_bessel_y0
Bessel function Y0 (x) |
| s17adc | 1 |
nag_bessel_y1
Bessel function Y1 (x) |
| s17aec | 1 |
nag_bessel_j0
Bessel function J0 (x) |
| s17afc | 1 |
nag_bessel_j1
Bessel function J1 (x) |
| s17agc | 1 |
nag_airy_ai
Airy function Ai(x) |
| s17ahc | 1 |
nag_airy_bi
Airy function Bi(x) |
| s17ajc | 1 |
nag_airy_ai_deriv
Airy function Ai'(x) |
| s17akc | 1 |
nag_airy_bi_deriv
Airy function Bi'(x) |
| s17alc | 6 |
nag_bessel_zeros
Zeros of Bessel functions Jα(x), J'α(x), Yα(x) or Y'α(x) |
| s17dcc | 7 |
nag_complex_bessel_y
Bessel functions Yν+a(z), real a ≥ 0, complex z, ν =0,1, 2,... |
| s17dec | 7 |
nag_complex_bessel_j
Bessel functions Jν+a(z), real a ≥ 0, complex z, ν =0,1, 2,... |
| s17dgc | 7 |
nag_complex_airy_ai
Airy functions Ai(z) and Ai'(z) , complex z |
| s17dhc | 7 |
nag_complex_airy_bi
Airy functions Bi(z) and Bi'(z) , complex z |
| s17dlc | 7 |
nag_complex_hankel
Hankel functions Hν+a(j)(z), j=1,2, real a ≥ 0, complex z, ν =0,1,2,... |
| s18acc | 1 |
nag_bessel_k0
Modified Bessel function K0 (x) |
| s18adc | 1 |
nag_bessel_k1
Modified Bessel function K1 (x) |
| s18aec | 1 |
nag_bessel_i0
Modified Bessel function I0 (x) |
| s18afc | 1 |
nag_bessel_i1
Modified Bessel function I1(x) |
| s18ccc | 2 |
nag_bessel_k0_scaled
Scaled modified Bessel function exK0(x) |
| s18cdc | 2 |
nag_bessel_k1_scaled
Scaled modified Bessel function exK1(x) |
| s18cec | 2 |
nag_bessel_i0_scaled
Scaled modified Bessel function e-|x|I0(x) |
| s18cfc | 2 |
nag_bessel_i1_scaled
Scaled modified Bessel function e-|x|I1(x) |
| s18dcc | 7 |
nag_complex_bessel_k
Modified Bessel functions Kν+a(z), real a ≥ 0, complex z, ν =0,1,2,... |
| s18dec | 7 |
nag_complex_bessel_i
Modified Bessel functions Iν+a(z), real a ≥ 0, complex z, ν =0,1,2,... |
| s18ecc | 6 |
nag_bessel_i_nu_scaled
Scaled modified Bessel function e-x Iν/4 (x) |
| s18edc | 6 |
nag_bessel_k_nu_scaled
Scaled modified Bessel function ex Kν/4 (x) |
| s18eec | 6 |
nag_bessel_i_nu
Modified Bessel function Iν/4 (x) |
| s18efc | 6 |
nag_bessel_k_nu
Modified Bessel function Kν/4 (x) |
| s18egc | 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 | 6 |
nag_bessel_k_alpha_scaled
Scaled modified Bessel functions Kα+n (x) for real x > 0, selected values of α ≥ 0 and n = 0,1,...,N |
| s18ejc | 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 | 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 | 7 |
nag_complex_bessel_j_seq
Bessel function of the 1st kind Jα ± n(z) |
| s19aac | 1 |
nag_kelvin_ber
Kelvin function ber x |
| s19abc | 1 |
nag_kelvin_bei
Kelvin function bei x |
| s19acc | 1 |
nag_kelvin_ker
Kelvin function ker x |
| s19adc | 1 |
nag_kelvin_kei
Kelvin function kei x |
| s20acc | 1 |
nag_fresnel_s
Fresnel integral S(x) |
| s20adc | 1 |
nag_fresnel_c
Fresnel integral C(x) |
| s21bac | 1 |
nag_elliptic_integral_rc
Degenerate symmetrised elliptic integral of 1st kind RC(x,y) |
| s21bbc | 1 |
nag_elliptic_integral_rf
Symmetrised elliptic integral of 1st kind RF(x,y,z) |
| s21bcc | 1 |
nag_elliptic_integral_rd
Symmetrised elliptic integral of 2nd kind RD(x,y,z) |
| s21bdc | 1 |
nag_elliptic_integral_rj
Symmetrised elliptic integral of 3rd kind RJ(x,y,z,r) |
| s21cac | 7 |
nag_real_jacobian_elliptic
Jacobian elliptic functions sn, cn and dn of real argument |
| s21cbc | 6 |
nag_jacobian_elliptic
Jacobian elliptic functions sn, cn and dn of complex argument |
| s21ccc | 6 |
nag_jacobian_theta
Jacobian theta functions with real arguments |
| s21dac | 6 |
nag_elliptic_integral_f
Elliptic integrals of the second kind with complex arguments |
| s22aac | 6 |
nag_legendre_p
Legendre and associated Legendre functions of the first kind with real arguments |