sl: A scientific library

Table of contents

1. Special functions
   1. Gamma function and related
   2. Polynomials and related
   3. Elliptic integrals and related

Special functions

Namespace sl::sf, or sl_sf as a standalone crate.

Gamma function and related

fn gamma(x: f64) -> f64

The gamma function Γ(x).

fn cgamma(z: c64) -> c64

The complex gamma function Γ(z).

Polynomial functions and related

fn legendre(n: i32, m: i32, x: f64) -> f64

Associated legendre function P_n,m(x). Legendre polynomial P_n(x)=P_n,0(x).

Elliptic integrals and related

fn agm(x: f64, y: f64) -> f64

Arithmetic-geometric mean of x and y.

fn cK(m: f64) -> f64

Complete elliptic integral of the first kind, m=k².

fn cE(m: f64) -> f64

Complete elliptic integral of the second kind, m=k².

fn eiF(phi: f64, m: f64) -> f64

Elliptic integral of the second kind, m=k².

fn eiE(phi: f64, m: f64) -> f64

Elliptic integral of the second kind, m=k².

fn eiPi(phi: f64, n: f64, m: f64) -> f64

Elliptic integral of the third kind, m=k².

fn RF(x: f64, y: f64, z: f6) -> f64

Carlson symmetric form R_F(x,y,z).

fn RC(x: f64, y: f64, z: f6) -> f64

Carlson symmetric form R_C(x,y).

fn RJ(x: f64, y: f64, z: f6, p: f64) -> f64

Carlson symmetric form R_J(x,y,z,p).

fn RD(x: f64, y: f64, z: f6) -> f64

Carlson symmetric form R_D(x,y,z).