libocamlgsl-ocaml-dev 1.19.1-1 / usr / lib / ocaml / gsl / gsl_sf.mli

(* gsl-ocaml - OCaml interface to GSL                       *)
(* Copyright (©) 2002-2012 - Olivier Andrieu                *)
(* Distributed under the terms of the GPL version 3         *)

(** Special functions *)

open Gsl_fun

(* AIRY functions *)
external airy_Ai : float -> mode -> float = "ml_gsl_sf_airy_Ai"
external airy_Ai_e : float -> mode -> result = "ml_gsl_sf_airy_Ai_e"

external airy_Bi : float -> mode -> float = "ml_gsl_sf_airy_Bi"
external airy_Bi_e : float -> mode -> result = "ml_gsl_sf_airy_Bi_e"

external airy_Ai_scaled : float -> mode -> float = "ml_gsl_sf_airy_Ai_scaled"
external airy_Ai_scaled_e : float -> mode -> result
  = "ml_gsl_sf_airy_Ai_scaled_e"

external airy_Bi_scaled : float -> mode -> float = "ml_gsl_sf_airy_Bi_scaled"
external airy_Bi_scaled_e : float -> mode -> result
  = "ml_gsl_sf_airy_Bi_scaled_e"

external airy_Ai_deriv : float -> mode -> float = "ml_gsl_sf_airy_Ai_deriv"
external airy_Ai_deriv_e : float -> mode -> result
  = "ml_gsl_sf_airy_Ai_deriv_e"

external airy_Bi_deriv : float -> mode -> float = "ml_gsl_sf_airy_Bi_deriv"
external airy_Bi_deriv_e : float -> mode -> result
  = "ml_gsl_sf_airy_Bi_deriv_e"

external airy_Ai_deriv_scaled : float -> mode -> float
  = "ml_gsl_sf_airy_Ai_deriv_scaled"
external airy_Ai_deriv_scaled_e : float -> mode -> result
  = "ml_gsl_sf_airy_Ai_deriv_scaled_e"

external airy_Bi_deriv_scaled : float -> mode -> float
  = "ml_gsl_sf_airy_Bi_deriv_scaled"
external airy_Bi_deriv_scaled_e : float -> mode -> result
  = "ml_gsl_sf_airy_Bi_deriv_scaled_e"


external airy_zero_Ai : int -> float = "ml_gsl_sf_airy_zero_Ai"
external airy_zero_Ai_e : int -> result = "ml_gsl_sf_airy_zero_Ai_e"

external airy_zero_Bi : int -> float = "ml_gsl_sf_airy_zero_Bi"
external airy_zero_Bi_e : int -> result = "ml_gsl_sf_airy_zero_Bi_e"


(* BESSEL functions *)
external bessel_J0 : float -> float = "ml_gsl_sf_bessel_J0"
external bessel_J0_e : float -> result = "ml_gsl_sf_bessel_J0_e"
external bessel_J1 : float -> float = "ml_gsl_sf_bessel_J1"
external bessel_J1_e : float -> result = "ml_gsl_sf_bessel_J1_e"
external bessel_Jn : int -> float -> float = "ml_gsl_sf_bessel_Jn"
external bessel_Jn_e : int -> float -> result = "ml_gsl_sf_bessel_Jn_e"
external bessel_Jn_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_Jn_array"

external bessel_Y0 : float -> float = "ml_gsl_sf_bessel_Y0"
external bessel_Y0_e : float -> result = "ml_gsl_sf_bessel_Y0_e"
external bessel_Y1 : float -> float = "ml_gsl_sf_bessel_Y1"
external bessel_Y1_e : float -> result = "ml_gsl_sf_bessel_Y1_e"
external bessel_Yn : int -> float -> float = "ml_gsl_sf_bessel_Yn"
external bessel_Yn_e : int -> float -> result = "ml_gsl_sf_bessel_Yn_e"
external bessel_Yn_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_Yn_array"

external bessel_I0 : float -> float = "ml_gsl_sf_bessel_I0"
external bessel_I0_e : float -> result = "ml_gsl_sf_bessel_I0_e"
external bessel_I1 : float -> float = "ml_gsl_sf_bessel_I1"
external bessel_I1_e : float -> result = "ml_gsl_sf_bessel_I1_e"
external bessel_In : int -> float -> float = "ml_gsl_sf_bessel_In"
external bessel_In_e : int -> float -> result = "ml_gsl_sf_bessel_In_e"
external bessel_In_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_In_array"

external bessel_K0 : float -> float = "ml_gsl_sf_bessel_K0"
external bessel_K0_e : float -> result = "ml_gsl_sf_bessel_K0_e"
external bessel_K1 : float -> float = "ml_gsl_sf_bessel_K1"
external bessel_K1_e : float -> result = "ml_gsl_sf_bessel_K1_e"
external bessel_Kn : int -> float -> float = "ml_gsl_sf_bessel_Kn"
external bessel_Kn_e : int -> float -> result = "ml_gsl_sf_bessel_Kn_e"
external bessel_Kn_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_Kn_array"

external bessel_I0_scaled : float -> float = "ml_gsl_sf_bessel_I0_scaled"
external bessel_I0_scaled_e : float -> result
  = "ml_gsl_sf_bessel_I0_scaled_e"
external bessel_I1_scaled : float -> float = "ml_gsl_sf_bessel_I1_scaled"
external bessel_I1_scaled_e : float -> result
  = "ml_gsl_sf_bessel_I1_scaled_e"
external bessel_In_scaled : int -> float -> float
  = "ml_gsl_sf_bessel_In_scaled"
external bessel_In_scaled_e : int -> float -> result
  = "ml_gsl_sf_bessel_In_scaled_e"
external bessel_In_scaled_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_In_scaled_array"

external bessel_K0_scaled : float -> float = "ml_gsl_sf_bessel_K0_scaled"
external bessel_K0_scaled_e : float -> result
  = "ml_gsl_sf_bessel_K0_scaled_e"
external bessel_K1_scaled : float -> float = "ml_gsl_sf_bessel_K1_scaled"
external bessel_K1_scaled_e : float -> result
  = "ml_gsl_sf_bessel_K1_scaled_e"
external bessel_Kn_scaled : int -> float -> float
  = "ml_gsl_sf_bessel_Kn_scaled"
external bessel_Kn_scaled_e : int -> float -> result
  = "ml_gsl_sf_bessel_Kn_scaled_e"
external bessel_Kn_scaled_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_Kn_scaled_array"


external bessel_j0 : float -> float = "ml_gsl_sf_bessel_j0"
external bessel_j0_e : float -> result = "ml_gsl_sf_bessel_j0_e"
external bessel_j1 : float -> float = "ml_gsl_sf_bessel_j1"
external bessel_j1_e : float -> result = "ml_gsl_sf_bessel_j1_e"
external bessel_j2 : float -> float = "ml_gsl_sf_bessel_j2"
external bessel_j2_e : float -> result = "ml_gsl_sf_bessel_j2_e"
external bessel_jl : int -> float -> float = "ml_gsl_sf_bessel_jl"
external bessel_jl_e : int -> float -> result = "ml_gsl_sf_bessel_jl_e"
external bessel_jl_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_jl_array"

external bessel_jl_steed_array : float -> float array -> unit
  = "ml_gsl_sf_bessel_jl_steed_array"

external bessel_y0 : float -> float = "ml_gsl_sf_bessel_y0"
external bessel_y0_e : float -> result = "ml_gsl_sf_bessel_y0_e"
external bessel_y1 : float -> float = "ml_gsl_sf_bessel_y1"
external bessel_y1_e : float -> result = "ml_gsl_sf_bessel_y1_e"
external bessel_y2 : float -> float = "ml_gsl_sf_bessel_y2"
external bessel_y2_e : float -> result = "ml_gsl_sf_bessel_y2_e"
external bessel_yl : int -> float -> float = "ml_gsl_sf_bessel_yl"
external bessel_yl_e : int -> float -> result = "ml_gsl_sf_bessel_yl_e"
external bessel_yl_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_yl_array"

external bessel_i0_scaled : float -> float = "ml_gsl_sf_bessel_i0_scaled"
external bessel_i0_scaled_e : float -> result
  = "ml_gsl_sf_bessel_i0_scaled_e"
external bessel_i1_scaled : float -> float = "ml_gsl_sf_bessel_i1_scaled"
external bessel_i1_scaled_e : float -> result
  = "ml_gsl_sf_bessel_i1_scaled_e"
external bessel_il_scaled : int -> float -> float
  = "ml_gsl_sf_bessel_il_scaled"
external bessel_il_scaled_e : int -> float -> result
  = "ml_gsl_sf_bessel_il_scaled_e"
external bessel_il_scaled_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_il_scaled_array"

external bessel_k0_scaled : float -> float = "ml_gsl_sf_bessel_k0_scaled"
external bessel_k0_scaled_e : float -> result
  = "ml_gsl_sf_bessel_k0_scaled_e"
external bessel_k1_scaled : float -> float = "ml_gsl_sf_bessel_k1_scaled"
external bessel_k1_scaled_e : float -> result
  = "ml_gsl_sf_bessel_k1_scaled_e"
external bessel_kl_scaled : int -> float -> float
  = "ml_gsl_sf_bessel_kl_scaled"
external bessel_kl_scaled_e : int -> float -> result
  = "ml_gsl_sf_bessel_kl_scaled_e"
external bessel_kl_scaled_array : int -> float -> float array -> unit
  = "ml_gsl_sf_bessel_kl_scaled_array"


external bessel_Jnu : float -> float -> float = "ml_gsl_sf_bessel_Jnu"
external bessel_Jnu_e : float -> float -> result = "ml_gsl_sf_bessel_Jnu_e"

external bessel_sequence_Jnu_e : float -> mode -> float array -> unit
  = "ml_gsl_sf_bessel_sequence_Jnu_e"

external bessel_Ynu : float -> float -> float = "ml_gsl_sf_bessel_Ynu"
external bessel_Ynu_e : float -> float -> result = "ml_gsl_sf_bessel_Ynu_e"

external bessel_Inu : float -> float -> float = "ml_gsl_sf_bessel_Inu"
external bessel_Inu_e : float -> float -> result = "ml_gsl_sf_bessel_Inu_e"

external bessel_Inu_scaled : float -> float -> float
  = "ml_gsl_sf_bessel_Inu_scaled"
external bessel_Inu_scaled_e : float -> float -> result
  = "ml_gsl_sf_bessel_Inu_scaled_e"

external bessel_Knu : float -> float -> float = "ml_gsl_sf_bessel_Knu"
external bessel_Knu_e : float -> float -> result = "ml_gsl_sf_bessel_Knu_e"

external bessel_lnKnu : float -> float -> float = "ml_gsl_sf_bessel_lnKnu"
external bessel_lnKnu_e : float -> float -> result
  = "ml_gsl_sf_bessel_lnKnu_e"

external bessel_Knu_scaled : float -> float -> float
  = "ml_gsl_sf_bessel_Knu_scaled"
external bessel_Knu_scaled_e : float -> float -> result
  = "ml_gsl_sf_bessel_Knu_scaled_e"


external bessel_zero_J0 : int -> float = "ml_gsl_sf_bessel_zero_J0"
external bessel_zero_J0_e : int -> result = "ml_gsl_sf_bessel_zero_J0_e"

external bessel_zero_J1 : int -> float = "ml_gsl_sf_bessel_zero_J1"
external bessel_zero_J1_e : int -> result = "ml_gsl_sf_bessel_zero_J1_e"

external bessel_zero_Jnu : float -> int -> float
  = "ml_gsl_sf_bessel_zero_Jnu"
external bessel_zero_Jnu_e : float -> int -> result
  = "ml_gsl_sf_bessel_zero_Jnu_e"


(* CLAUSEN functions *)
external clausen : float -> float = "ml_gsl_sf_clausen"
external clausen_e : float -> result = "ml_gsl_sf_clausen_e"


(* COULOMB functions *)
external hydrogenicR_1 : float -> float -> float = "ml_gsl_sf_hydrogenicR_1"
external hydrogenicR_1_e : float -> float -> result
  = "ml_gsl_sf_hydrogenicR_1_e"

external hydrogenicR : int -> int -> float -> float -> float
  = "ml_gsl_sf_hydrogenicR"
external hydrogenicR_e : int -> int -> float -> float -> result
  = "ml_gsl_sf_hydrogenicR_e"

(* FIXME: COULOMB wave functions *)
external coulomb_CL_e : float -> float -> result = "ml_gsl_sf_coulomb_CL_e"

external coulomb_CL_array : float -> float -> float array -> unit
  = "ml_gsl_sf_coulomb_CL_array"


(* FIXME: coupling coeffs *)

(* DAWSON functions *)
external dawson : float -> float = "ml_gsl_sf_dawson"
external dawson_e : float -> result = "ml_gsl_sf_dawson_e"


(* DEBYE functions *)
external debye_1 : float -> float = "ml_gsl_sf_debye_1"
external debye_1_e : float -> result = "ml_gsl_sf_debye_1_e"

external debye_2 : float -> float = "ml_gsl_sf_debye_2"
external debye_2_e : float -> result = "ml_gsl_sf_debye_2_e"

external debye_3 : float -> float = "ml_gsl_sf_debye_3"
external debye_3_e : float -> result = "ml_gsl_sf_debye_3_e"

external debye_4 : float -> float = "ml_gsl_sf_debye_4"
external debye_4_e : float -> result = "ml_gsl_sf_debye_4_e"

external debye_5 : float -> float = "ml_gsl_sf_debye_5"
external debye_5_e : float -> result = "ml_gsl_sf_debye_5_e"

external debye_6 : float -> float = "ml_gsl_sf_debye_6"
external debye_6_e : float -> result = "ml_gsl_sf_debye_6_e"


(* DILOGARITHM *)
external dilog : float -> float = "ml_gsl_sf_dilog"
external dilog_e : float -> result = "ml_gsl_sf_dilog_e"

external complex_dilog_xy_e : float -> float -> result * result
  = "ml_gsl_sf_complex_dilog_xy_e"

external complex_dilog_e : float -> float -> result * result
  = "ml_gsl_sf_complex_dilog_e"

external complex_spence_xy_e : float -> float -> result * result
  = "ml_gsl_sf_complex_spence_xy_e"


(* ELEMENTARY operations *)
external multiply_e : float -> float -> result = "ml_gsl_sf_multiply_e"

external multiply_err_e : x:float -> dx:float -> y:float -> dy:float -> result
  = "ml_gsl_sf_multiply_err_e"


(* ELLIPTIC integrals *)
external ellint_Kcomp : float -> mode -> float = "ml_gsl_sf_ellint_Kcomp"
external ellint_Kcomp_e : float -> mode -> result
  = "ml_gsl_sf_ellint_Kcomp_e"

external ellint_Ecomp : float -> mode -> float = "ml_gsl_sf_ellint_Ecomp"
external ellint_Ecomp_e : float -> mode -> result
  = "ml_gsl_sf_ellint_Ecomp_e"

external ellint_Pcomp : float -> float -> mode -> float
  = "ml_gsl_sf_ellint_Pcomp"
external ellint_Pcomp_e : float -> float -> mode -> result
  = "ml_gsl_sf_ellint_Pcomp_e"

external ellint_Dcomp : float -> mode -> float = "ml_gsl_sf_ellint_Dcomp"
external ellint_Dcomp_e : float -> mode -> result
  = "ml_gsl_sf_ellint_Dcomp_e"

external ellint_F : float -> float -> mode -> float = "ml_gsl_sf_ellint_F"
external ellint_F_e : float -> float -> mode -> result
  = "ml_gsl_sf_ellint_F_e"

external ellint_E : float -> float -> mode -> float = "ml_gsl_sf_ellint_E"
external ellint_E_e : float -> float -> mode -> result
  = "ml_gsl_sf_ellint_E_e"

external ellint_P : float -> float -> float -> mode -> float
  = "ml_gsl_sf_ellint_P"
external ellint_P_e : float -> float -> float -> mode -> result
  = "ml_gsl_sf_ellint_P_e"

external ellint_D : float -> float -> mode -> float = "ml_gsl_sf_ellint_D"
external ellint_D_e : float -> float -> mode -> result
  = "ml_gsl_sf_ellint_D_e"

external ellint_RC : float -> float -> mode -> float = "ml_gsl_sf_ellint_RC"
external ellint_RC_e : float -> float -> mode -> result
  = "ml_gsl_sf_ellint_RC_e"

external ellint_RD : float -> float -> float -> mode -> float
  = "ml_gsl_sf_ellint_RD"
external ellint_RD_e : float -> float -> float -> mode -> result
  = "ml_gsl_sf_ellint_RD_e"

external ellint_RF : float -> float -> float -> mode -> float
  = "ml_gsl_sf_ellint_RF"
external ellint_RF_e : float -> float -> float -> mode -> result
  = "ml_gsl_sf_ellint_RF_e"

external ellint_RJ : float -> float -> float -> float -> mode -> float
  = "ml_gsl_sf_ellint_RJ"
external ellint_RJ_e : float -> float -> float -> float -> mode -> result
  = "ml_gsl_sf_ellint_RJ_e"

(* FIXME: elljac_e *)

(* ERROR function *)
external erf : float -> float = "ml_gsl_sf_erf" "gsl_sf_erf" "float"
external erf_e : float -> result = "ml_gsl_sf_erf_e"

external erfc : float -> float = "ml_gsl_sf_erfc" "gsl_sf_erfc" "float"
external erfc_e : float -> result = "ml_gsl_sf_erfc_e"

external log_erfc : float -> float
  = "ml_gsl_sf_log_erfc" "gsl_sf_log_erfc" "float"
external log_erfc_e : float -> result = "ml_gsl_sf_log_erfc_e"

external erf_Z : float -> float = "ml_gsl_sf_erf_Z" "gsl_sf_erf_Z" "float"
external erf_Z_e : float -> result = "ml_gsl_sf_erf_Z_e"

external erf_Q : float -> float = "ml_gsl_sf_erf_Q" "gsl_sf_erf_Q" "float"
external erf_Q_e : float -> result = "ml_gsl_sf_erf_Q_e"


(* EXPONENTIAL functions *)
external exp : float -> float = "ml_gsl_sf_exp" "gsl_sf_exp" "float"
external exp_e : float -> result = "ml_gsl_sf_exp_e"

external exp_e10 : float -> result_e10 = "ml_gsl_sf_exp_e10_e"

external exp_mult : float -> float -> float = "ml_gsl_sf_exp_mult"
external exp_mult_e : float -> float -> result = "ml_gsl_sf_exp_mult_e"

external exp_mult_e10 : float -> float -> result_e10
  = "ml_gsl_sf_exp_mult_e10_e"


external expm1 : float -> float = "ml_gsl_sf_expm1"
external expm1_e : float -> result = "ml_gsl_sf_expm1_e"

external exprel : float -> float = "ml_gsl_sf_exprel"
external exprel_e : float -> result = "ml_gsl_sf_exprel_e"

external exprel_2 : float -> float = "ml_gsl_sf_exprel_2"
external exprel_2_e : float -> result = "ml_gsl_sf_exprel_2_e"

external exprel_n : int -> float -> float = "ml_gsl_sf_exprel_n"
external exprel_n_e : int -> float -> result = "ml_gsl_sf_exprel_n_e"

external exp_err_e : x:float -> dx:float -> result = "ml_gsl_sf_exp_err_e"

external exp_err_e10 : x:float -> dx:float -> result_e10
  = "ml_gsl_sf_exp_err_e10_e"

external exp_mult_err_e : x:float -> dx:float -> y:float -> dy:float -> result
  = "ml_gsl_sf_exp_mult_err_e"

external exp_mult_err_e10_e : x:float -> dx:float -> y:float -> dy:float -> result_e10
  = "ml_gsl_sf_exp_mult_err_e10_e"


(* EXPONENTIAL integrals *)
external expint_E1 : float -> float = "ml_gsl_sf_expint_E1"
external expint_E1_e : float -> result = "ml_gsl_sf_expint_E1_e"

external expint_E2 : float -> float = "ml_gsl_sf_expint_E2"
external expint_E2_e : float -> result = "ml_gsl_sf_expint_E2_e"

external expint_E1_scaled : float -> float = "ml_gsl_sf_expint_E1_scaled"
external expint_E1_scaled_e : float -> result
  = "ml_gsl_sf_expint_E1_scaled_e"

external expint_E2_scaled : float -> float = "ml_gsl_sf_expint_E2_scaled"
external expint_E2_scaled_e : float -> result
  = "ml_gsl_sf_expint_E2_scaled_e"

external expint_Ei : float -> float = "ml_gsl_sf_expint_Ei"
external expint_Ei_e : float -> result = "ml_gsl_sf_expint_Ei_e"

external expint_Ei_scaled : float -> float = "ml_gsl_sf_expint_Ei_scaled"
external expint_Ei_scaled_e : float -> result
  = "ml_gsl_sf_expint_Ei_scaled_e"

external shi : float -> float = "ml_gsl_sf_Shi"

external chi : float -> float = "ml_gsl_sf_Chi"

external expint_3 : float -> float = "ml_gsl_sf_expint_3"
external expint_3_e : float -> result = "ml_gsl_sf_expint_3_e"

external si : float -> float = "ml_gsl_sf_Si"

external ci : float -> float = "ml_gsl_sf_Ci"

external atanint : float -> float = "ml_gsl_sf_atanint"
external atanint_e : float -> result = "ml_gsl_sf_atanint_e"


(* fermi-dirac *)
external fermi_dirac_m1 : float -> float = "ml_gsl_sf_fermi_dirac_m1"
external fermi_dirac_m1_e : float -> result = "ml_gsl_sf_fermi_dirac_m1_e"

external fermi_dirac_0 : float -> float = "ml_gsl_sf_fermi_dirac_0"
external fermi_dirac_0_e : float -> result = "ml_gsl_sf_fermi_dirac_0_e"

external fermi_dirac_1 : float -> float = "ml_gsl_sf_fermi_dirac_1"
external fermi_dirac_1_e : float -> result = "ml_gsl_sf_fermi_dirac_1_e"

external fermi_dirac_2 : float -> float = "ml_gsl_sf_fermi_dirac_2"
external fermi_dirac_2_e : float -> result = "ml_gsl_sf_fermi_dirac_2_e"

external fermi_dirac_int : int -> float -> float
  = "ml_gsl_sf_fermi_dirac_int"
external fermi_dirac_int_e : int -> float -> result
  = "ml_gsl_sf_fermi_dirac_int_e"

external fermi_dirac_mhalf : float -> float = "ml_gsl_sf_fermi_dirac_mhalf"
external fermi_dirac_mhalf_e : float -> result
  = "ml_gsl_sf_fermi_dirac_mhalf_e"

external fermi_dirac_half : float -> float = "ml_gsl_sf_fermi_dirac_half"
external fermi_dirac_half_e : float -> result
  = "ml_gsl_sf_fermi_dirac_half_e"

external fermi_dirac_3half : float -> float = "ml_gsl_sf_fermi_dirac_3half"
external fermi_dirac_3half_e : float -> result
  = "ml_gsl_sf_fermi_dirac_3half_e"

external fermi_dirac_inc_0 : float -> float -> float
  = "ml_gsl_sf_fermi_dirac_inc_0"
external fermi_dirac_inc_0_e : float -> float -> result
  = "ml_gsl_sf_fermi_dirac_inc_0_e"


(* Gamma function *)
external gamma : float -> float = "ml_gsl_sf_gamma"

external gamma_e : float -> result = "ml_gsl_sf_gamma_e"

external lngamma : float -> float = "ml_gsl_sf_lngamma"
external lngamma_e : float -> result = "ml_gsl_sf_lngamma_e"

external lngamma_sgn_e : float -> result * float = "ml_gsl_sf_lngamma_sgn_e"

external gammastar : float -> float = "ml_gsl_sf_gammastar"
external gammastar_e : float -> result = "ml_gsl_sf_gammastar_e"

external gammainv : float -> float = "ml_gsl_sf_gammainv"
external gammainv_e : float -> result = "ml_gsl_sf_gammainv_e"

external lngamma_complex_e : float -> float -> result * result
  = "ml_gsl_sf_lngamma_complex_e"

external taylorcoeff : int -> float -> float = "ml_gsl_sf_taylorcoeff"
external taylorcoeff_e : int -> float -> result = "ml_gsl_sf_taylorcoeff_e"

external fact : int -> float = "ml_gsl_sf_fact"
external fact_e : int -> result = "ml_gsl_sf_fact_e"

external doublefact : int -> float = "ml_gsl_sf_doublefact"
external doublefact_e : int -> result = "ml_gsl_sf_doublefact_e"

external lnfact : int -> float = "ml_gsl_sf_lnfact"
external lnfact_e : int -> result = "ml_gsl_sf_lnfact_e"

external lndoublefact : int -> float = "ml_gsl_sf_lndoublefact"
external lndoublefact_e : int -> result = "ml_gsl_sf_lndoublefact_e"

external choose : int -> int -> float = "ml_gsl_sf_choose"
external choose_e : int -> int -> result = "ml_gsl_sf_choose_e"

external lnchoose : int -> int -> float = "ml_gsl_sf_lnchoose"
external lnchoose_e : int -> int -> result = "ml_gsl_sf_lnchoose_e"

external poch : float -> float -> float = "ml_gsl_sf_poch"
external poch_e : float -> float -> result = "ml_gsl_sf_poch_e"

external lnpoch : float -> float -> float = "ml_gsl_sf_lnpoch"
external lnpoch_e : float -> float -> result = "ml_gsl_sf_lnpoch_e"

external lnpoch_sgn_e : float -> float -> result * float
  = "ml_gsl_sf_lngamma_sgn_e"

external pochrel : float -> float -> float = "ml_gsl_sf_pochrel"
external pochrel_e : float -> float -> result = "ml_gsl_sf_pochrel_e"

external gamma_inc_Q : float -> float -> float = "ml_gsl_sf_gamma_inc_Q"
external gamma_inc_Q_e : float -> float -> result = "ml_gsl_sf_gamma_inc_Q_e"

external gamma_inc_P : float -> float -> float = "ml_gsl_sf_gamma_inc_P"
external gamma_inc_P_e : float -> float -> result = "ml_gsl_sf_gamma_inc_P_e"

external gamma_inc : float -> float -> float = "ml_gsl_sf_gamma_inc"
external gamma_inc_e : float -> float -> result = "ml_gsl_sf_gamma_inc_e"

external beta : float -> float -> float = "ml_gsl_sf_beta"
external beta_e : float -> float -> result = "ml_gsl_sf_beta_e"

external lnbeta : float -> float -> float = "ml_gsl_sf_lnbeta"
external lnbeta_e : float -> float -> result = "ml_gsl_sf_lnbeta_e"

external lnbeta_sgn_e : float -> float -> result * float
  = "ml_gsl_sf_lnbeta_sgn_e"

external beta_inc : float -> float -> float -> float = "ml_gsl_sf_beta_inc"
external beta_inc_e : float -> float -> float -> result
  = "ml_gsl_sf_beta_inc_e"


(* GEGENBAUER functions *)
external gegenpoly_1 : float -> float -> float = "ml_gsl_sf_gegenpoly_1"
external gegenpoly_1_e : float -> float -> result = "ml_gsl_sf_gegenpoly_1_e"

external gegenpoly_2 : float -> float -> float = "ml_gsl_sf_gegenpoly_2"
external gegenpoly_2_e : float -> float -> result = "ml_gsl_sf_gegenpoly_2_e"

external gegenpoly_3 : float -> float -> float = "ml_gsl_sf_gegenpoly_3"
external gegenpoly_3_e : float -> float -> result = "ml_gsl_sf_gegenpoly_3_e"

external gegenpoly_n : int -> float -> float -> float
  = "ml_gsl_sf_gegenpoly_n"
external gegenpoly_n_e : int -> float -> float -> result
  = "ml_gsl_sf_gegenpoly_n_e"

external gegenpoly_array : float -> float -> float array -> unit
  = "ml_gsl_sf_gegenpoly_array"


(* HYPERGEOMETRIC functions *)
(* FIXME *)

(* LAGUERRE functions *)
external laguerre_1 : float -> float -> float = "ml_gsl_sf_laguerre_1"
external laguerre_1_e : float -> float -> result = "ml_gsl_sf_laguerre_1_e"

external laguerre_2 : float -> float -> float = "ml_gsl_sf_laguerre_2"
external laguerre_2_e : float -> float -> result = "ml_gsl_sf_laguerre_2_e"

external laguerre_3 : float -> float -> float = "ml_gsl_sf_laguerre_3"
external laguerre_3_e : float -> float -> result = "ml_gsl_sf_laguerre_3_e"

external laguerre_n : int -> float -> float -> float = "ml_gsl_sf_laguerre_n"
external laguerre_n_e : int -> float -> float -> result
  = "ml_gsl_sf_laguerre_n_e"


(* LAMBERT W functions *)
external lambert_W0 : float -> float = "ml_gsl_sf_lambert_W0"
external lambert_W0_e : float -> result = "ml_gsl_sf_lambert_W0_e"

external lambert_Wm1 : float -> float = "ml_gsl_sf_lambert_Wm1"
external lambert_Wm1_e : float -> result = "ml_gsl_sf_lambert_Wm1_e"


(* LEGENDRE functions *)
external legendre_P1 : float -> float = "ml_gsl_sf_legendre_P1"
external legendre_P1_e : float -> result = "ml_gsl_sf_legendre_P1_e"

external legendre_P2 : float -> float = "ml_gsl_sf_legendre_P2"
external legendre_P2_e : float -> result = "ml_gsl_sf_legendre_P2_e"

external legendre_P3 : float -> float = "ml_gsl_sf_legendre_P3"
external legendre_P3_e : float -> result = "ml_gsl_sf_legendre_P3_e"

external legendre_Pl : int -> float -> float = "ml_gsl_sf_legendre_Pl"
external legendre_Pl_e : int -> float -> result = "ml_gsl_sf_legendre_Pl_e"

external legendre_Pl_array : float -> float array -> unit
  = "ml_gsl_sf_legendre_Pl_array"

external legendre_Q0 : float -> float = "ml_gsl_sf_legendre_Q0"
external legendre_Q0_e : float -> result = "ml_gsl_sf_legendre_Q0_e"

external legendre_Q1 : float -> float = "ml_gsl_sf_legendre_Q1"
external legendre_Q1_e : float -> result = "ml_gsl_sf_legendre_Q1_e"

external legendre_Ql : int -> float -> float = "ml_gsl_sf_legendre_Ql"
external legendre_Ql_e : int -> float -> result = "ml_gsl_sf_legendre_Ql_e"


(* Associated LEGENDRE functions *)
external legendre_Plm : int -> int -> float -> float
  = "ml_gsl_sf_legendre_Plm"
external legendre_Plm_e : int -> int -> float -> result
  = "ml_gsl_sf_legendre_Plm_e"

(* FIXME: linking problem with GSL 2.0 *)
(* <:ext< legendre_Plm_array@ml_gsl_sf_legendre_Plm_array,int,int,float,float array,unit >> *)
external legendre_sphPlm : int -> int -> float -> float
  = "ml_gsl_sf_legendre_sphPlm"
external legendre_sphPlm_e : int -> int -> float -> result
  = "ml_gsl_sf_legendre_sphPlm_e"

(* FIXME: linking problem with GSL 2.0 *)
(* <:ext< legendre_sphPlm_array@ml_gsl_sf_legendre_sphPlm_array,int,int,float,float array,unit >> *)
(* FIXME: linking problem with GSL 2.0 *)
(* <:ext< legendre_array_size@ml_gsl_sf_legendre_array_size,int,int,int >> *)

(* LOGARITHM and related functions *)
external log : float -> float = "ml_gsl_sf_log"
external log_e : float -> result = "ml_gsl_sf_log_e"

external log_abs : float -> float = "ml_gsl_sf_log_abs"
external log_abs_e : float -> result = "ml_gsl_sf_log_abs_e"

external log_complex_e : float -> float -> result * result
  = "ml_gsl_sf_complex_log_e"

external log_1plusx : float -> float = "ml_gsl_sf_log_1plusx"
external log_1plusx_e : float -> result = "ml_gsl_sf_log_1plusx_e"

external log_1plusx_mx : float -> float = "ml_gsl_sf_log_1plusx_mx"
external log_1plusx_mx_e : float -> result = "ml_gsl_sf_log_1plusx_mx_e"


(* POWER function *)
external pow_int : float -> int -> float = "ml_gsl_sf_pow_int"
external pow_int_e : float -> int -> result = "ml_gsl_sf_pow_int_e"


(* PSI function *)
external psi_int : int -> float = "ml_gsl_sf_psi_int"
external psi_int_e : int -> result = "ml_gsl_sf_psi_int_e"

external psi : float -> float = "ml_gsl_sf_psi"
external psi_e : float -> result = "ml_gsl_sf_psi_e"

external psi_1piy : float -> float = "ml_gsl_sf_psi_1piy"
external psi_1piy_e : float -> result = "ml_gsl_sf_psi_1piy_e"

external psi_complex_e : float -> float -> result * result
  = "ml_gsl_sf_complex_psi_e"

external psi_1_int : int -> float = "ml_gsl_sf_psi_1_int"
external psi_1_int_e : int -> result = "ml_gsl_sf_psi_1_int_e"

external psi_1 : float -> float = "ml_gsl_sf_psi_1"
external psi_1_e : float -> result = "ml_gsl_sf_psi_1_e"

external psi_n : int -> float -> float = "ml_gsl_sf_psi_n"
external psi_n_e : int -> float -> result = "ml_gsl_sf_psi_n_e"


(* SYNCHROTRON functions *)
external synchrotron_1 : float -> float = "ml_gsl_sf_synchrotron_1"
external synchrotron_1_e : float -> result = "ml_gsl_sf_synchrotron_1_e"

external synchrotron_2 : float -> float = "ml_gsl_sf_synchrotron_2"
external synchrotron_2_e : float -> result = "ml_gsl_sf_synchrotron_2_e"


(* TRANSPORT functions *)
external transport_2 : float -> float = "ml_gsl_sf_transport_2"
external transport_2_e : float -> result = "ml_gsl_sf_transport_2_e"

external transport_3 : float -> float = "ml_gsl_sf_transport_3"
external transport_3_e : float -> result = "ml_gsl_sf_transport_3_e"

external transport_4 : float -> float = "ml_gsl_sf_transport_4"
external transport_4_e : float -> result = "ml_gsl_sf_transport_4_e"

external transport_5 : float -> float = "ml_gsl_sf_transport_5"
external transport_5_e : float -> result = "ml_gsl_sf_transport_5_e"


(* TRIGONOMETRIC functions *)
external sin : float -> float = "ml_gsl_sf_sin" "gsl_sf_sin" "float"
external sin_e : float -> result = "ml_gsl_sf_sin_e"

external cos : float -> float = "ml_gsl_sf_cos" "gsl_sf_cos" "float"
external cos_e : float -> result = "ml_gsl_sf_cos_e"

external hypot : float -> float -> float = "ml_gsl_sf_hypot"
external hypot_e : float -> float -> result = "ml_gsl_sf_hypot_e"

external sinc : float -> float = "ml_gsl_sf_sinc" "gsl_sf_sinc" "float"
external sinc_e : float -> result = "ml_gsl_sf_sinc_e"

external complex_sin_e : float -> float -> result * result
  = "ml_gsl_sf_complex_sin_e"

external complex_cos_e : float -> float -> result * result
  = "ml_gsl_sf_complex_cos_e"

external complex_logsin_e : float -> float -> result * result
  = "ml_gsl_sf_complex_logsin_e"

external lnsinh : float -> float = "ml_gsl_sf_lnsinh"
external lnsinh_e : float -> result = "ml_gsl_sf_lnsinh_e"

external lncosh : float -> float = "ml_gsl_sf_lncosh"
external lncosh_e : float -> result = "ml_gsl_sf_lncosh_e"

external rect_of_polar : r:float -> theta:float -> result * result
  = "ml_gsl_sf_polar_to_rect"

external polar_of_rect : x:float -> y:float -> result * result
  = "ml_gsl_sf_rect_to_polar"

external angle_restrict_symm : float -> float
  = "ml_gsl_sf_angle_restrict_symm"

external angle_restrict_pos : float -> float = "ml_gsl_sf_angle_restrict_pos"

external sin_err_e : float -> dx:float -> result = "ml_gsl_sf_sin_err_e"

external cos_err_e : float -> dx:float -> result = "ml_gsl_sf_cos_err_e"


(* ZETA functions *)
external zeta_int : int -> float = "ml_gsl_sf_zeta_int"
external zeta_int_e : int -> result = "ml_gsl_sf_zeta_int_e"

external zeta : float -> float = "ml_gsl_sf_zeta"
external zeta_e : float -> result = "ml_gsl_sf_zeta_e"

external hzeta : float -> float -> float = "ml_gsl_sf_hzeta"
external hzeta_e : float -> float -> result = "ml_gsl_sf_hzeta_e"

external eta_int : int -> float = "ml_gsl_sf_eta_int"
external eta_int_e : int -> result = "ml_gsl_sf_eta_int_e"

external eta : float -> float = "ml_gsl_sf_eta"
external eta_e : float -> result = "ml_gsl_sf_eta_e"