Struct LegendrePolynomial 

pub struct LegendrePolynomial;

Legendre polynomials P_n(x) and Gauss-Legendre quadrature.

Provides evaluation via the three-term recurrence, computation of all P_0, …, P_n, and Gauss-Legendre nodes and weights up to degree n.

Implementations

impl LegendrePolynomial

pub fn eval(n: usize, x: f64) -> f64

Evaluate P_n(x) using the three-term recurrence.

pub fn eval_all(n: usize, x: f64) -> Vec<f64>

Evaluate P_0(x), …, P_n(x) and return all values.

pub fn gauss_legendre(n: usize) -> (Vec<f64>, Vec<f64>)

Compute the n-point Gauss-Legendre nodes and weights on [-1, 1].

Uses Newton’s method to find roots of P_n and computes weights from the derivative formula. Returns (nodes, weights).

pub fn integrate<F: Fn(f64) -> f64>(f: F, n: usize) -> f64

Integrate f over [-1, 1] using n-point Gauss-Legendre quadrature.