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Module Maths

module Maths: sig .. end
Mathematics module

This module contains some basic and advanced mathematical operations. If you cannot find some function in this module, try Stats module.

Please refer to GSL documentation using following linke for details: https://www.gnu.org/software/gsl/manual


Basic math functions

val abs : float -> float
val sqrt : float -> float
val pow : float -> float -> float
val exp : float -> float
val expm1 : float -> float
val exp_mult : float -> float -> float
val exprel : float -> float
val ln : float -> float
val ln1p : float -> float
val ln_abs : float -> float
val log2 : float -> float
val log10 : float -> float
val log : float -> float -> float

Trigonometric Functions

val sin : float -> float
val cos : float -> float
val tan : float -> float
val cot : float -> float
val sec : float -> float
val csc : float -> float
val asin : float -> float
val acos : float -> float
val atan : float -> float
val acot : float -> float
val sinh : float -> float
val cosh : float -> float
val asinh : float -> float
val acosh : float -> float
val atanh : float -> float
val sinc : float -> float
val lnsinh : float -> float
val lncosh : float -> float
val hypot : float -> float -> float
val rect_of_polar : r:float -> theta:float -> float * float
val polar_of_rect : x:float -> y:float -> float * float
val angle_restrict_symm : float -> float
val angle_restrict_pos : float -> float

Airy functions and derivatives

val airy_Ai : float -> float
val airy_Bi : float -> float
val airy_Ai_scaled : float -> float
val airy_Bi_scaled : float -> float
val airy_Ai_deriv : float -> float
val airy_Bi_deriv : float -> float
val airy_Ai_deriv : float -> float
val airy_Bi_deriv : float -> float
val airy_zero_Ai : int -> float
val airy_zero_Bi : int -> float

Regular Cylindrical Bessel Functions

val bessel_J0 : float -> float
val bessel_J1 : float -> float
val bessel_Jn : int -> float -> float
val bessel_Jn_array : int -> int -> float -> float array

Irregular Cylindrical Bessel Functions

val bessel_Y0 : float -> float
val bessel_Y1 : float -> float
val bessel_Yn : int -> float -> float
val bessel_Yn_array : int -> int -> float -> float array

Regular Modified Cylindrical Bessel Functions

val bessel_I0 : float -> float
val bessel_I1 : float -> float
val bessel_In : int -> float -> float
val bessel_In_array : int -> int -> float -> float array
val bessel_I0_scaled : float -> float
val bessel_I1_scaled : float -> float
val bessel_In_scaled : int -> float -> float
val bessel_In_scaled_array : int -> int -> float -> float array

Irregular Modified Cylindrical Bessel Functions

val bessel_K0 : float -> float
val bessel_K1 : float -> float
val bessel_Kn : int -> float -> float
val bessel_Kn_array : int -> int -> float -> float array
val bessel_K0_scaled : float -> float
val bessel_K1_scaled : float -> float
val bessel_Kn_scaled : int -> float -> float
val bessel_Kn_scaled_array : int -> int -> float -> float array

Regular Spherical Bessel Functions

val bessel_j0 : float -> float
val bessel_j1 : float -> float
val bessel_j2 : float -> float
val bessel_jl : int -> float -> float
val bessel_jl_array : int -> float -> float array
val bessel_jl_steed_array : int -> float -> float array

Irregular Spherical Bessel Functions

val bessel_y0 : float -> float
val bessel_y1 : float -> float
val bessel_y2 : float -> float
val bessel_yl : int -> float -> float
val bessel_yl_array : int -> float -> float array

Regular Modified Spherical Bessel Functions

val bessel_i0_scaled : float -> float
val bessel_i1_scaled : float -> float
val bessel_il_scaled : int -> float -> float
val bessel_il_array_scaled : int -> float -> float array

Irregular Modified Spherical Bessel Functions

val bessel_k0_scaled : float -> float
val bessel_k1_scaled : float -> float
val bessel_kl_scaled : int -> float -> float
val bessel_kl_array_scaled : int -> float -> float array

Regular Bessel Function - Fractional Order

val bessel_Jnu : float -> float -> float

Irregular Bessel Functions - Fractional Order

val bessel_Ynu : float -> float -> float

Regular Modified Bessel Functions - Fractional Order

val bessel_Inu : float -> float -> float
val bessel_Inu_scaled : float -> float -> float

Irregular Modified Bessel Functions - Fractional Order

val bessel_Knu : float -> float -> float
val bessel_lnKnu : float -> float -> float
val bessel_Knu_scaled : float -> float -> float

Zeros of Regular Bessel Functions

val bessel_zero_J0 : int -> float
val bessel_zero_J1 : int -> float
val bessel_zero_Jnu : float -> int -> float

Clausen Functions

val clausen : float -> float

Dawson Function

val dawson : float -> float

Debye Functions

val debye_1 : float -> float
val debye_2 : float -> float
val debye_3 : float -> float
val debye_4 : float -> float
val debye_5 : float -> float
val debye_6 : float -> float

Dilogarithm

val dilog : float -> float

Elliptic Integrals

val ellint_Kcomp : float -> float
val ellint_Ecomp : float -> float
val ellint_Pcomp : float -> float -> float
val ellint_Dcomp : float -> float

Elliptic Integrals - Legendre Form of Complete Elliptic Integrals

val laguerre_1 : float -> float -> float
val laguerre_2 : float -> float -> float
val laguerre_3 : float -> float -> float
val laguerre_n : int -> float -> float -> float

Elliptic Integrals - Legendre Form of Incomplete Elliptic Integrals

val ellint_F : float -> float -> float
val ellint_E : float -> float -> float
val ellint_P : float -> float -> float -> float
val ellint_D : float -> float -> float

Elliptic Integrals - Carlson Forms of Incomplete Elliptic Integrals

val ellint_RC : float -> float -> float
val ellint_RD : float -> float -> float -> float
val ellint_RF : float -> float -> float -> float
val ellint_RJ : float -> float -> float -> float -> float

Exponential Integrals

val expint_E1 : float -> float
val expint_E2 : float -> float
val expint_Ei : float -> float
val expint_E1_scaled : float -> float
val expint_E2_scaled : float -> float
val expint_Ei_scaled : float -> float
val expint_3 : float -> float
val shi : float -> float
val chi : float -> float
val si : float -> float
val ci : float -> float
val atanint : float -> float

Fermi-Dirac Function

val fermi_dirac_m1 : float -> float
val fermi_dirac_0 : float -> float
val fermi_dirac_1 : float -> float
val fermi_dirac_2 : float -> float
val fermi_dirac_int : int -> float -> float
val fermi_dirac_mhalf : float -> float
val fermi_dirac_half : float -> float
val fermi_dirac_3half : float -> float
val fermi_dirac_inc_0 : float -> float -> float

Gamma Functions

val gamma : float -> float
val lngamma : float -> float
val gammastar : float -> float
val gammainv : float -> float

Incomplete Gamma Functions

val gamma_inc : float -> float -> float
val gamma_inc_Q : float -> float -> float
val gamma_inc_P : float -> float -> float

Factorials

val factorial : int -> float
val double_factorial : int -> float
val ln_factorial : int -> float
val ln_double_factorial : int -> float
val combination : int -> int -> float
val ln_combination : int -> int -> float
val taylorcoeff : int -> float -> float

Pochhammer Symbol

val poch : float -> float -> float
val lnpoch : float -> float -> float
val pochrel : float -> float -> float

Beta functions

val betaf : float -> float -> float
val lnbeta : float -> float -> float
val beta_inc : float -> float -> float -> float

Laguerre Functions

val laguerre_1 : float -> float -> float
val laguerre_2 : float -> float -> float
val laguerre_3 : float -> float -> float
val laguerre_n : int -> float -> float -> float

Lambert W Functions

val lambert_w0 : float -> float
val lambert_w1 : float -> float

Legendre Functions and Spherical Harmonics

val legendre_P1 : float -> float
val legendre_P2 : float -> float
val legendre_P3 : float -> float
val legendre_Pl : int -> float -> float
val legendre_Pl_array : int -> float -> float array
val legendre_Q0 : float -> float
val legendre_Q1 : float -> float
val legendre_Ql : int -> float -> float

Psi (Digamma) Function

val psi : float -> float
val psi_int : int -> float
val psi_1 : float -> float
val psi_1piy : float -> float
val psi_1_pint : int -> float
val psi_n : int -> float -> float

Synchrotron Functions

val synchrotron_1 : float -> float
val synchrotron_2 : float -> float

Transport Functions

val transport_2 : float -> float
val transport_3 : float -> float
val transport_4 : float -> float
val transport_5 : float -> float

Zeta Functions

val zeta : float -> float
val zeta_int : int -> float
val hzeta : float -> float -> float
val eta : float -> float
val eta_int : int -> float