Function eval_jacobi 

pub fn eval_jacobi<N, Z: JacobiArg<N>>(n: N, alpha: f64, beta: f64, z: Z) -> Z

Evaluate Jacobi polynomial $P_n^{(\alpha, \beta)}$ at a point.

This is a translation of the scipy.special.eval_jacobi Cython implementation into Rust.

Definition

The Jacobi polynomials can be defined via the Gauss hypergeometric function $_2F_1$ as

$$ P_n^{(\alpha, \beta)}(z) = {n + \alpha \choose n} \, \hyp{2}{1}{-n,\enspace n+1+\alpha+\beta}{1+\alpha}{-{z-1 \over 2}} $$

When $n$ is an integer the result is a polynomial of degree $n$. See Abramowitz & Stegun 22.5.42 ¹ or DLMF 18.5.7 ² for details.

See also

• eval_legendre: Evaluate Legendre polynomials, $P_n$
• hyp2f1: Gauss’ hypergeometric function, $_2F_1$

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1. Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972. ↩

2. NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/18.5.E7 ↩