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5. gslsf: The GSL Special Functions Module

The special function module, gslsf, wraps nearly 200 GSL special functions. Since the special functions are described in detail in the documentation for the GSL library, no attempt will be made here to duplicate the main documentation. Rather, a description of how the special functions have been wrapped by the module is given.

GSL prefixes the special functions with the string gsl_sf_. This prefix is omitted from the corresponding intrinsic functions of the gslsf module. For example, the GSL function that computes spherical harmonics is called gsl_sf_legendre_sphPlm. However, it is represented in the module by simply legendre_sphPlm.

Most of GSL's special functions take scalar arguments and returns a scalar. For example, gsl_sf_legendre_sphPlm takes three arguments (int, int, and a double) and returns a double, e.g.,

    int l = 5, m = 0;
    double x = 0.5;
    double y = gsl_sf_legendre_sphPlm (l, m, x);
While the module supports the scalar usage, e.g,
    variable l = 5, m = 0, x = 0.5;
    variable y = legendre_sphPlm (l, m, x);
it also supports vector arguments, e.g.,
    variable l = 5, m = 0, x = [-1:1:0.1];
    variable y = legendre_sphPlm (l, m, x);
and
    variable l = 5, m = [0:l], x = 0.5;
    variable y = legendre_sphPlm (l, m, x);

Some of the functions are expensive to compute to full double precision accuracy. In the interest of speed, it may want to perform perform the computation with less precision. Hence, several of the special functions take an optional mode argument that specifies the desired precision: GSL_PREC_DOUBLE for double precision accuracy, GSL_PREC_SINGLE for single precision accuracy, and GSL_PREC_APPROX for a relative accuracy of 5e-4. For example, to compute the Airy function to double precision accuracy use:

     y = airy_Ai (x, GSL_PREC_DOUBLE);
If called without the mode argument, i.e.,
     y = airy_Ai (x);
the function will be computed to a default precision of GSL_PREC_SINGLE. The default precision can be set and queried by the gslsf_set_precision and gslsf_get_precision functions, resp. Functions that do not take the optional mode argument will always be computed at full precision.

5.1 Airy Functions

airy_Ai

Synopsis

S-Lang version of gsl_sf_airy_Ai

Usage

Double_Type[] airy_Ai (Double_Type[] x [,Int_Type mode])

airy_Ai_deriv

Synopsis

S-Lang version of gsl_sf_airy_Ai_deriv

Usage

Double_Type[] airy_Ai_deriv (Double_Type[] x [,Int_Type mode])

airy_Ai_deriv_scaled

Synopsis

S-Lang version of gsl_sf_airy_Ai_deriv_scaled

Usage

Double_Type[] airy_Ai_deriv_scaled (Double_Type[] x [,Int_Type mode])

airy_Ai_scaled

Synopsis

S-Lang version of gsl_sf_airy_Ai_scaled

Usage

Double_Type[] airy_Ai_scaled (Double_Type[] x [,Int_Type mode])

airy_Bi

Synopsis

S-Lang version of gsl_sf_airy_Bi

Usage

Double_Type[] airy_Bi (Double_Type[] x [,Int_Type mode])

airy_Bi_deriv

Synopsis

S-Lang version of gsl_sf_airy_Bi_deriv

Usage

Double_Type[] airy_Bi_deriv (Double_Type[] x [,Int_Type mode])

airy_Bi_deriv_scaled

Synopsis

S-Lang version of gsl_sf_airy_Bi_deriv_scaled

Usage

Double_Type[] airy_Bi_deriv_scaled (Double_Type[] x [,Int_Type mode])

airy_Bi_scaled

Synopsis

S-Lang version of gsl_sf_airy_Bi_scaled

Usage

Double_Type[] airy_Bi_scaled (Double_Type[] x [,Int_Type mode])

5.2 Bessel Functions

bessel_I0

Synopsis

S-Lang version of gsl_sf_bessel_I0

Usage

Double_Type[] bessel_I0 (Double_Type[] x)

bessel_I0_scaled

Synopsis

S-Lang version of gsl_sf_bessel_I0_scaled

Usage

Double_Type[] bessel_I0_scaled (Double_Type[] x)

bessel_i0_scaled

Synopsis

S-Lang version of gsl_sf_bessel_i0_scaled

Usage

Double_Type[] bessel_i0_scaled (Double_Type[] x)

bessel_I1

Synopsis

S-Lang version of gsl_sf_bessel_I1

Usage

Double_Type[] bessel_I1 (Double_Type[] x)

bessel_i1_scaled

Synopsis

S-Lang version of gsl_sf_bessel_i1_scaled

Usage

Double_Type[] bessel_i1_scaled (Double_Type[] x)

bessel_I1_scaled

Synopsis

S-Lang version of gsl_sf_bessel_I1_scaled

Usage

Double_Type[] bessel_I1_scaled (Double_Type[] x)

bessel_i2_scaled

Synopsis

S-Lang version of gsl_sf_bessel_i2_scaled

Usage

Double_Type[] bessel_i2_scaled (Double_Type[] x)

bessel_il_scaled

Synopsis

S-Lang version of gsl_sf_bessel_il_scaled

Usage

Double_Type[] bessel_il_scaled (Int_Type[] l, Double_Type[] x)

bessel_In

Synopsis

S-Lang version of gsl_sf_bessel_In

Usage

Double_Type[] bessel_In (Int_Type[] n, Double_Type[] x)

bessel_In_scaled

Synopsis

S-Lang version of gsl_sf_bessel_In_scaled

Usage

Double_Type[] bessel_In_scaled (Int_Type[] n, Double_Type[] x)

bessel_Inu

Synopsis

S-Lang version of gsl_sf_bessel_Inu

Usage

Double_Type[] bessel_Inu (Double_Type[] nu, Double_Type[] x)

bessel_Inu_scaled

Synopsis

S-Lang version of gsl_sf_bessel_Inu_scaled

Usage

Double_Type[] bessel_Inu_scaled (Double_Type[] nu, Double_Type[] x)

bessel_J0

Synopsis

S-Lang version of gsl_sf_bessel_J0

Usage

Double_Type[] bessel_J0 (Double_Type[] x)

bessel_j0

Synopsis

S-Lang version of gsl_sf_bessel_j0

Usage

Double_Type[] bessel_j0 (Double_Type[] x)

bessel_j1

Synopsis

S-Lang version of gsl_sf_bessel_j1

Usage

Double_Type[] bessel_j1 (Double_Type[] x)

bessel_J1

Synopsis

S-Lang version of gsl_sf_bessel_J1

Usage

Double_Type[] bessel_J1 (Double_Type[] x)

bessel_j2

Synopsis

S-Lang version of gsl_sf_bessel_j2

Usage

Double_Type[] bessel_j2 (Double_Type[] x)

bessel_jl

Synopsis

S-Lang version of gsl_sf_bessel_jl

Usage

Double_Type[] bessel_jl (Int_Type[] l, Double_Type[] x)

bessel_Jn

Synopsis

S-Lang version of gsl_sf_bessel_Jn

Usage

Double_Type[] bessel_Jn (Int_Type[] n, Double_Type[] x)

bessel_Jnu

Synopsis

S-Lang version of gsl_sf_bessel_Jnu

Usage

Double_Type[] bessel_Jnu (Double_Type[] nu, Double_Type[] x)

bessel_K0

Synopsis

S-Lang version of gsl_sf_bessel_K0

Usage

Double_Type[] bessel_K0 (Double_Type[] x)

bessel_K0_scaled

Synopsis

S-Lang version of gsl_sf_bessel_K0_scaled

Usage

Double_Type[] bessel_K0_scaled (Double_Type[] x)

bessel_k0_scaled

Synopsis

S-Lang version of gsl_sf_bessel_k0_scaled

Usage

Double_Type[] bessel_k0_scaled (Double_Type[] x)

bessel_K1

Synopsis

S-Lang version of gsl_sf_bessel_K1

Usage

Double_Type[] bessel_K1 (Double_Type[] x)

bessel_K1_scaled

Synopsis

S-Lang version of gsl_sf_bessel_K1_scaled

Usage

Double_Type[] bessel_K1_scaled (Double_Type[] x)

bessel_k1_scaled

Synopsis

S-Lang version of gsl_sf_bessel_k1_scaled

Usage

Double_Type[] bessel_k1_scaled (Double_Type[] x)

bessel_k2_scaled

Synopsis

S-Lang version of gsl_sf_bessel_k2_scaled

Usage

Double_Type[] bessel_k2_scaled (Double_Type[] x)

bessel_kl_scaled

Synopsis

S-Lang version of gsl_sf_bessel_kl_scaled

Usage

Double_Type[] bessel_kl_scaled (Int_Type[] l, Double_Type[] x)

bessel_Kn

Synopsis

S-Lang version of gsl_sf_bessel_Kn

Usage

Double_Type[] bessel_Kn (Int_Type[] n, Double_Type[] x)

bessel_Kn_scaled

Synopsis

S-Lang version of gsl_sf_bessel_Kn_scaled

Usage

Double_Type[] bessel_Kn_scaled (Int_Type[] n, Double_Type[] x)

bessel_Knu

Synopsis

S-Lang version of gsl_sf_bessel_Knu

Usage

Double_Type[] bessel_Knu (Double_Type[] nu, Double_Type[] x)

bessel_Knu_scaled

Synopsis

S-Lang version of gsl_sf_bessel_Knu_scaled

Usage

Double_Type[] bessel_Knu_scaled (Double_Type[] nu, Double_Type[] x)

bessel_lnKnu

Synopsis

S-Lang version of gsl_sf_bessel_lnKnu

Usage

Double_Type[] bessel_lnKnu (Double_Type[] nu, Double_Type[] x)

bessel_Y0

Synopsis

S-Lang version of gsl_sf_bessel_Y0

Usage

Double_Type[] bessel_Y0 (Double_Type[] x)

bessel_y0

Synopsis

S-Lang version of gsl_sf_bessel_y0

Usage

Double_Type[] bessel_y0 (Double_Type[] x)

bessel_y1

Synopsis

S-Lang version of gsl_sf_bessel_y1

Usage

Double_Type[] bessel_y1 (Double_Type[] x)

bessel_Y1

Synopsis

S-Lang version of gsl_sf_bessel_Y1

Usage

Double_Type[] bessel_Y1 (Double_Type[] x)

bessel_y2

Synopsis

S-Lang version of gsl_sf_bessel_y2

Usage

Double_Type[] bessel_y2 (Double_Type[] x)

bessel_yl

Synopsis

S-Lang version of gsl_sf_bessel_yl

Usage

Double_Type[] bessel_yl (Int_Type[] l, Double_Type[] x)

bessel_Yn

Synopsis

S-Lang version of gsl_sf_bessel_Yn

Usage

Double_Type[] bessel_Yn (Int_Type[] n, Double_Type[] x)

bessel_Ynu

Synopsis

S-Lang version of gsl_sf_bessel_Ynu

Usage

Double_Type[] bessel_Ynu (Double_Type[] nu, Double_Type[] x)

5.3 Beta Functions

beta

Synopsis

S-Lang version of gsl_sf_beta

Usage

Double_Type[] beta (Double_Type[] a, Double_Type[] b)

beta_inc

Synopsis

S-Lang version of gsl_sf_beta_inc

Usage

Double_Type[] beta_inc (Double_Type[] a, Double_Type[] b, Double_Type[] x)

lnbeta

Synopsis

S-Lang version of gsl_sf_lnbeta

Usage

Double_Type[] lnbeta (Double_Type[] a, Double_Type[] b)

5.4 Clausen Functions

clausen

Synopsis

S-Lang version of gsl_sf_clausen

Usage

Double_Type[] clausen (Double_Type[] x)

5.5 Conical Functions

conicalP_0

Synopsis

S-Lang version of gsl_sf_conicalP_0

Usage

Double_Type[] conicalP_0 (Double_Type[] lambda, Double_Type[] x)

conicalP_1

Synopsis

S-Lang version of gsl_sf_conicalP_1

Usage

Double_Type[] conicalP_1 (Double_Type[] lambda, Double_Type[] x)

conicalP_cyl_reg

Synopsis

S-Lang version of gsl_sf_conicalP_cyl_reg

Usage

Double_Type[] conicalP_cyl_reg (m, lambda, x)

  Int_Type[] m
  Double_Type[] lambda
  Double_Type[] x

conicalP_half

Synopsis

S-Lang version of gsl_sf_conicalP_half

Usage

Double_Type[] conicalP_half (Double_Type[] lambda, Double_Type[] x)

conicalP_mhalf

Synopsis

S-Lang version of gsl_sf_conicalP_mhalf

Usage

Double_Type[] conicalP_mhalf (Double_Type[] lambda, Double_Type[] x)

conicalP_sph_reg

Synopsis

S-Lang version of gsl_sf_conicalP_sph_reg

Usage

Double_Type[] conicalP_sph_reg (l, lambda, x)

  Int_Type[] l
  Double_Type[] lambda
  Double_Type[] x

5.6 Coulomb Functions

hydrogenicR

Synopsis

S-Lang version of gsl_sf_hydrogenicR

Usage

Double_Type[] hydrogenicR (n, l, Z, r)

  Int_Type[] n
  Int_Type[] l
  Double_Type[] Z
  Double_Type[] r

hydrogenicR_1

Synopsis

S-Lang version of gsl_sf_hydrogenicR_1

Usage

Double_Type[] hydrogenicR_1 (Double_Type[] Z, Double_Type[] r)

5.7 Debye Functions

debye_1

Synopsis

S-Lang version of gsl_sf_debye_1

Usage

Double_Type[] debye_1 (Double_Type[] x)

debye_2

Synopsis

S-Lang version of gsl_sf_debye_2

Usage

Double_Type[] debye_2 (Double_Type[] x)

debye_3

Synopsis

S-Lang version of gsl_sf_debye_3

Usage

Double_Type[] debye_3 (Double_Type[] x)

debye_4

Synopsis

S-Lang version of gsl_sf_debye_4

Usage

Double_Type[] debye_4 (Double_Type[] x)

5.8 Di/Tri and Polygamma Functions

psi

Synopsis

S-Lang version of gsl_sf_psi

Usage

Double_Type[] psi (Double_Type[] x)

psi_1_int

Synopsis

S-Lang version of gsl_sf_psi_1_int

Usage

Double_Type[] psi_1_int (Int_Type[] n)

psi_1piy

Synopsis

S-Lang version of gsl_sf_psi_1piy

Usage

Double_Type[] psi_1piy (Double_Type[] y)

psi_int

Synopsis

S-Lang version of gsl_sf_psi_int

Usage

Double_Type[] psi_int (Int_Type[] n)

psi_n

Synopsis

S-Lang version of gsl_sf_psi_n

Usage

Double_Type[] psi_n (Int_Type[] n, Double_Type[] x)

5.9 Elliptic Integrals

ellint_D

Synopsis

S-Lang version of gsl_sf_ellint_D

Usage

Double_Type[] ellint_D (phi, k, n [,mode])

  Double_Type[] phi
  Double_Type[] k
  Double_Type[] n 
  Int_Type mode

ellint_E

Synopsis

S-Lang version of gsl_sf_ellint_E

Usage

Double_Type[] ellint_E (phi, k [,mode])

  Double_Type[] phi
  Double_Type[] k 
  Int_Type mode

ellint_Ecomp

Synopsis

S-Lang version of gsl_sf_ellint_Ecomp

Usage

Double_Type[] ellint_Ecomp (Double_Type[] k [,Int_Type mode])

ellint_F

Synopsis

S-Lang version of gsl_sf_ellint_F

Usage

Double_Type[] ellint_F (phi, k [,mode])

  Double_Type[] phi
  Double_Type[] k 
  Int_Type mode

ellint_Kcomp

Synopsis

S-Lang version of gsl_sf_ellint_Kcomp

Usage

Double_Type[] ellint_Kcomp (Double_Type[] k [,Int_Type mode])

ellint_P

Synopsis

S-Lang version of gsl_sf_ellint_P

Usage

Double_Type[] ellint_P (phi, k, n [,mode])

  Double_Type[] phi
  Double_Type[] k
  Double_Type[] n 
  Int_Type mode

ellint_RC

Synopsis

S-Lang version of gsl_sf_ellint_RC

Usage

Double_Type[] ellint_RC (Double_Type[] x, Double_Type[] y [,Int_Type mode])

ellint_RD

Synopsis

S-Lang version of gsl_sf_ellint_RD

Usage

Double_Type[] ellint_RD (x, y, z [,mode])

  Double_Type[] x
  Double_Type[] y
  Double_Type[] z 
  Int_Type mode

ellint_RF

Synopsis

S-Lang version of gsl_sf_ellint_RF

Usage

Double_Type[] ellint_RF (x, y, z [,mode])

  Double_Type[] x
  Double_Type[] y
  Double_Type[] z 
  Int_Type mode

ellint_RJ

Synopsis

S-Lang version of gsl_sf_ellint_RJ

Usage

Double_Type[] ellint_RJ (x, y, z, p [,mode])

  Double_Type[] x
  Double_Type[] y
  Double_Type[] z
  Double_Type[] p 
  Int_Type mode

5.10 Error Functions

erf

Synopsis

S-Lang version of gsl_sf_erf

Usage

Double_Type[] erf (Double_Type[] x)

erf_Q

Synopsis

S-Lang version of gsl_sf_erf_Q

Usage

Double_Type[] erf_Q (Double_Type[] x)

erf_Z

Synopsis

S-Lang version of gsl_sf_erf_Z

Usage

Double_Type[] erf_Z (Double_Type[] x)

erfc

Synopsis

S-Lang version of gsl_sf_erfc

Usage

Double_Type[] erfc (Double_Type[] x)

log_erfc

Synopsis

S-Lang version of gsl_sf_log_erfc

Usage

Double_Type[] log_erfc (Double_Type[] x)

5.11 Eta/Zeta Functions

eta

Synopsis

S-Lang version of gsl_sf_eta

Usage

Double_Type[] eta (Double_Type[] s)

eta_int

Synopsis

S-Lang version of gsl_sf_eta_int

Usage

Double_Type[] eta_int (Int_Type[] n)

hzeta

Synopsis

S-Lang version of gsl_sf_hzeta

Usage

Double_Type[] hzeta (Double_Type[] s, Double_Type[] q)

zeta

Synopsis

S-Lang version of gsl_sf_zeta

Usage

Double_Type[] zeta (Double_Type[] s)

zeta_int

Synopsis

S-Lang version of gsl_sf_zeta_int

Usage

Double_Type[] zeta_int (Int_Type[] n)

5.12 Exponential Functions and Integrals

exp_mult

Synopsis

S-Lang version of gsl_sf_exp_mult

Usage

Double_Type[] exp_mult (Double_Type[] x, Double_Type[] y)

expint_3

Synopsis

S-Lang version of gsl_sf_expint_3

Usage

Double_Type[] expint_3 (Double_Type[] x)

expint_E1

Synopsis

S-Lang version of gsl_sf_expint_E1

Usage

Double_Type[] expint_E1 (Double_Type[] x)

expint_E1_scaled

Synopsis

S-Lang version of gsl_sf_expint_E1_scaled

Usage

Double_Type[] expint_E1_scaled (Double_Type[] x)

expint_E2

Synopsis

S-Lang version of gsl_sf_expint_E2

Usage

Double_Type[] expint_E2 (Double_Type[] x)

expint_E2_scaled

Synopsis

S-Lang version of gsl_sf_expint_E2_scaled

Usage

Double_Type[] expint_E2_scaled (Double_Type[] x)

expint_Ei

Synopsis

S-Lang version of gsl_sf_expint_Ei

Usage

Double_Type[] expint_Ei (Double_Type[] x)

expint_Ei_scaled

Synopsis

S-Lang version of gsl_sf_expint_Ei_scaled

Usage

Double_Type[] expint_Ei_scaled (Double_Type[] x)

expm1

Synopsis

S-Lang version of gsl_sf_expm1

Usage

Double_Type[] expm1 (Double_Type[] x)

exprel

Synopsis

S-Lang version of gsl_sf_exprel

Usage

Double_Type[] exprel (Double_Type[] x)

exprel_2

Synopsis

S-Lang version of gsl_sf_exprel_2

Usage

Double_Type[] exprel_2 (Double_Type[] x)

exprel_n

Synopsis

S-Lang version of gsl_sf_exprel_n

Usage

Double_Type[] exprel_n (Int_Type[] n, Double_Type[] x)

5.13 Fermi-Dirac Functions

fermi_dirac_0

Synopsis

S-Lang version of gsl_sf_fermi_dirac_0

Usage

Double_Type[] fermi_dirac_0 (Double_Type[] x)

fermi_dirac_1

Synopsis

S-Lang version of gsl_sf_fermi_dirac_1

Usage

Double_Type[] fermi_dirac_1 (Double_Type[] x)

fermi_dirac_2

Synopsis

S-Lang version of gsl_sf_fermi_dirac_2

Usage

Double_Type[] fermi_dirac_2 (Double_Type[] x)

fermi_dirac_3half

Synopsis

S-Lang version of gsl_sf_fermi_dirac_3half

Usage

Double_Type[] fermi_dirac_3half (Double_Type[] x)

fermi_dirac_half

Synopsis

S-Lang version of gsl_sf_fermi_dirac_half

Usage

Double_Type[] fermi_dirac_half (Double_Type[] x)

fermi_dirac_inc_0

Synopsis

S-Lang version of gsl_sf_fermi_dirac_inc_0

Usage

Double_Type[] fermi_dirac_inc_0 (Double_Type[] x, Double_Type[] b)

fermi_dirac_int

Synopsis

S-Lang version of gsl_sf_fermi_dirac_int

Usage

Double_Type[] fermi_dirac_int (Int_Type[] j, Double_Type[] x)

fermi_dirac_m1

Synopsis

S-Lang version of gsl_sf_fermi_dirac_m1

Usage

Double_Type[] fermi_dirac_m1 (Double_Type[] x)

fermi_dirac_mhalf

Synopsis

S-Lang version of gsl_sf_fermi_dirac_mhalf

Usage

Double_Type[] fermi_dirac_mhalf (Double_Type[] x)

5.14 Gamma Functions

gamma

Synopsis

S-Lang version of gsl_sf_gamma

Usage

Double_Type[] gamma (Double_Type[] x)

gamma_inc

Synopsis

S-Lang version of gsl_sf_gamma_inc

Usage

Double_Type[] gamma_inc (Double_Type[] a, Double_Type[] x)

gamma_inc_P

Synopsis

S-Lang version of gsl_sf_gamma_inc_P

Usage

Double_Type[] gamma_inc_P (Double_Type[] a, Double_Type[] x)

gamma_inc_Q

Synopsis

S-Lang version of gsl_sf_gamma_inc_Q

Usage

Double_Type[] gamma_inc_Q (Double_Type[] a, Double_Type[] x)

gammainv

Synopsis

S-Lang version of gsl_sf_gammainv

Usage

Double_Type[] gammainv (Double_Type[] x)

gammastar

Synopsis

S-Lang version of gsl_sf_gammastar

Usage

Double_Type[] gammastar (Double_Type[] x)

lngamma

Synopsis

S-Lang version of gsl_sf_lngamma

Usage

Double_Type[] lngamma (Double_Type[] x)

5.15 Gegenbauer Functions

gegenpoly_1

Synopsis

S-Lang version of gsl_sf_gegenpoly_1

Usage

Double_Type[] gegenpoly_1 (Double_Type[] lambda, Double_Type[] x)

gegenpoly_2

Synopsis

S-Lang version of gsl_sf_gegenpoly_2

Usage

Double_Type[] gegenpoly_2 (Double_Type[] lambda, Double_Type[] x)

gegenpoly_3

Synopsis

S-Lang version of gsl_sf_gegenpoly_3

Usage

Double_Type[] gegenpoly_3 (Double_Type[] lambda, Double_Type[] x)

gegenpoly_n

Synopsis

S-Lang version of gsl_sf_gegenpoly_n

Usage

Double_Type[] gegenpoly_n (n, lambda, x)

  Int_Type[] n
  Double_Type[] lambda
  Double_Type[] x

5.16 Hypergeometric Functions

hyperg_0F1

Synopsis

S-Lang version of gsl_sf_hyperg_0F1

Usage

Double_Type[] hyperg_0F1 (Double_Type[] c, Double_Type[] x)

hyperg_1F1

Synopsis

S-Lang version of gsl_sf_hyperg_1F1

Usage

Double_Type[] hyperg_1F1 (a, b, x)

  Double_Type[] a
  Double_Type[] b
  Double_Type[] x

hyperg_1F1_int

Synopsis

S-Lang version of gsl_sf_hyperg_1F1_int

Usage

Double_Type[] hyperg_1F1_int (Int_Type[] m, Int_Type[] n, Double_Type[] x)

hyperg_2F0

Synopsis

S-Lang version of gsl_sf_hyperg_2F0

Usage

Double_Type[] hyperg_2F0 (a, b, x)

  Double_Type[] a
  Double_Type[] b
  Double_Type[] x

hyperg_2F1

Synopsis

S-Lang version of gsl_sf_hyperg_2F1

Usage

Double_Type[] hyperg_2F1 (a, b, c, x)

  Double_Type[] a
  Double_Type[] b
  Double_Type[] c
  Double_Type[] x

hyperg_2F1_conj

Synopsis

S-Lang version of gsl_sf_hyperg_2F1_conj

Usage

Double_Type[] hyperg_2F1_conj (aR, aI, c, x)

  Double_Type[] aR
  Double_Type[] aI
  Double_Type[] c
  Double_Type[] x

hyperg_2F1_conj_renorm

Synopsis

S-Lang version of gsl_sf_hyperg_2F1_conj_renorm

Usage

Double_Type[] hyperg_2F1_conj_renorm (aR, aI, c, x)

  Double_Type[] aR
  Double_Type[] aI
  Double_Type[] c
  Double_Type[] x

hyperg_2F1_renorm

Synopsis

S-Lang version of gsl_sf_hyperg_2F1_renorm

Usage

Double_Type[] hyperg_2F1_renorm (a, b, c, x)

  Double_Type[] a
  Double_Type[] b
  Double_Type[] c
  Double_Type[] x

hyperg_U

Synopsis

S-Lang version of gsl_sf_hyperg_U

Usage

Double_Type[] hyperg_U (Double_Type[] a, Double_Type[] b, Double_Type[] x)

hyperg_U_int

Synopsis

S-Lang version of gsl_sf_hyperg_U_int

Usage

Double_Type[] hyperg_U_int (Int_Type[] m, Int_Type[] n, Double_Type[] x)

5.17 Laguerre Functions

laguerre_1

Synopsis

S-Lang version of gsl_sf_laguerre_1

Usage

Double_Type[] laguerre_1 (Double_Type[] a, Double_Type[] x)

laguerre_2

Synopsis

S-Lang version of gsl_sf_laguerre_2

Usage

Double_Type[] laguerre_2 (Double_Type[] a, Double_Type[] x)

laguerre_3

Synopsis

S-Lang version of gsl_sf_laguerre_3

Usage

Double_Type[] laguerre_3 (Double_Type[] a, Double_Type[] x)

laguerre_n

Synopsis

S-Lang version of gsl_sf_laguerre_n

Usage

Double_Type[] laguerre_n (Int_Type[] n, Double_Type[] a, Double_Type[] x)

5.18 Lambert Functions

lambert_W0

Synopsis

S-Lang version of gsl_sf_lambert_W0

Usage

Double_Type[] lambert_W0 (Double_Type[] x)

lambert_Wm1

Synopsis

S-Lang version of gsl_sf_lambert_Wm1

Usage

Double_Type[] lambert_Wm1 (Double_Type[] x)

5.19 Legendre Functions and Spherical Harmonics

legendre_H3d

Synopsis

S-Lang version of gsl_sf_legendre_H3d

Usage

Double_Type[] legendre_H3d (l, lambda, eta)

  Int_Type[] l
  Double_Type[] lambda
  Double_Type[] eta

legendre_H3d_0

Synopsis

S-Lang version of gsl_sf_legendre_H3d_0

Usage

Double_Type[] legendre_H3d_0 (Double_Type[] lambda, Double_Type[] eta)

legendre_H3d_1

Synopsis

S-Lang version of gsl_sf_legendre_H3d_1

Usage

Double_Type[] legendre_H3d_1 (Double_Type[] lambda, Double_Type[] eta)

legendre_P1

Synopsis

S-Lang version of gsl_sf_legendre_P1

Usage

Double_Type[] legendre_P1 (Double_Type[] x)

legendre_P2

Synopsis

S-Lang version of gsl_sf_legendre_P2

Usage

Double_Type[] legendre_P2 (Double_Type[] x)

legendre_P3

Synopsis

S-Lang version of gsl_sf_legendre_P3

Usage

Double_Type[] legendre_P3 (Double_Type[] x)

legendre_Pl

Synopsis

S-Lang version of gsl_sf_legendre_Pl

Usage

Double_Type[] legendre_Pl (Int_Type[] l, Double_Type[] x)

legendre_Plm

Synopsis

S-Lang version of gsl_sf_legendre_Plm

Usage

Double_Type[] legendre_Plm (Int_Type[] l, Int_Type[] m, Double_Type[] x)

legendre_Q0

Synopsis

S-Lang version of gsl_sf_legendre_Q0

Usage

Double_Type[] legendre_Q0 (Double_Type[] x)

legendre_Q1

Synopsis

S-Lang version of gsl_sf_legendre_Q1

Usage

Double_Type[] legendre_Q1 (Double_Type[] x)

legendre_Ql

Synopsis

S-Lang version of gsl_sf_legendre_Ql

Usage

Double_Type[] legendre_Ql (Int_Type[] l, Double_Type[] x)

legendre_sphPlm

Synopsis

S-Lang version of gsl_sf_legendre_sphPlm

Usage

Double_Type[] legendre_sphPlm (Int_Type[] l, Int_Type[] m, Double_Type[] x)

5.20 Logarithm and Related Functions

log_1plusx

Synopsis

S-Lang version of gsl_sf_log_1plusx

Usage

Double_Type[] log_1plusx (Double_Type[] x)

log_1plusx_mx

Synopsis

S-Lang version of gsl_sf_log_1plusx_mx

Usage

Double_Type[] log_1plusx_mx (Double_Type[] x)

log_abs

Synopsis

S-Lang version of gsl_sf_log_abs

Usage

Double_Type[] log_abs (Double_Type[] x)

5.21 Transport Functions

transport_2

Synopsis

S-Lang version of gsl_sf_transport_2

Usage

Double_Type[] transport_2 (Double_Type[] x)

transport_3

Synopsis

S-Lang version of gsl_sf_transport_3

Usage

Double_Type[] transport_3 (Double_Type[] x)

transport_4

Synopsis

S-Lang version of gsl_sf_transport_4

Usage

Double_Type[] transport_4 (Double_Type[] x)

transport_5

Synopsis

S-Lang version of gsl_sf_transport_5

Usage

Double_Type[] transport_5 (Double_Type[] x)

5.22 Miscellaneous Functions

angle_restrict_pos

Synopsis

S-Lang version of gsl_sf_angle_restrict_pos

Usage

Double_Type[] angle_restrict_pos (Double_Type[] theta)

angle_restrict_symm

Synopsis

S-Lang version of gsl_sf_angle_restrict_symm

Usage

Double_Type[] angle_restrict_symm (Double_Type[] theta)

atanint

Synopsis

S-Lang version of gsl_sf_atanint

Usage

Double_Type[] atanint (Double_Type[] x)

Chi

Synopsis

S-Lang version of gsl_sf_Chi

Usage

Double_Type[] Chi (Double_Type[] x)

Ci

Synopsis

S-Lang version of gsl_sf_Ci

Usage

Double_Type[] Ci (Double_Type[] x)

dawson

Synopsis

S-Lang version of gsl_sf_dawson

Usage

Double_Type[] dawson (Double_Type[] x)

dilog

Synopsis

S-Lang version of gsl_sf_dilog

Usage

Double_Type[] dilog (Double_Type[] x)

hazard

Synopsis

S-Lang version of gsl_sf_hazard

Usage

Double_Type[] hazard (Double_Type[] x)

hypot

Synopsis

S-Lang version of gsl_sf_hypot

Usage

Double_Type[] hypot (Double_Type[] x, Double_Type[] y)

lncosh

Synopsis

S-Lang version of gsl_sf_lncosh

Usage

Double_Type[] lncosh (Double_Type[] x)

lnpoch

Synopsis

S-Lang version of gsl_sf_lnpoch

Usage

Double_Type[] lnpoch (Double_Type[] a, Double_Type[] x)

lnsinh

Synopsis

S-Lang version of gsl_sf_lnsinh

Usage

Double_Type[] lnsinh (Double_Type[] x)

poch

Synopsis

S-Lang version of gsl_sf_poch

Usage

Double_Type[] poch (Double_Type[] a, Double_Type[] x)

pochrel

Synopsis

S-Lang version of gsl_sf_pochrel

Usage

Double_Type[] pochrel (Double_Type[] a, Double_Type[] x)

Shi

Synopsis

S-Lang version of gsl_sf_Shi

Usage

Double_Type[] Shi (Double_Type[] x)

Si

Synopsis

S-Lang version of gsl_sf_Si

Usage

Double_Type[] Si (Double_Type[] x)

sinc

Synopsis

S-Lang version of gsl_sf_sinc

Usage

Double_Type[] sinc (Double_Type[] x)

synchrotron_1

Synopsis

S-Lang version of gsl_sf_synchrotron_1

Usage

Double_Type[] synchrotron_1 (Double_Type[] x)

synchrotron_2

Synopsis

S-Lang version of gsl_sf_synchrotron_2

Usage

Double_Type[] synchrotron_2 (Double_Type[] x)

taylorcoeff

Synopsis

S-Lang version of gsl_sf_taylorcoeff

Usage

Double_Type[] taylorcoeff (Int_Type[] n, Double_Type[] x)


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