Function evaluate_recurrence 

pub fn evaluate_recurrence(
    properties: &PolynomialProperties,
    n: usize,
    x: f64,
) -> f64

Evaluate polynomial using three-term recurrence relation

Generic implementation for all orthogonal polynomials that uses the recurrence relation defined in PolynomialProperties. This is mathematically the most stable approach for polynomial evaluation.

Recurrence Form

For orthogonal polynomials, the three-term recurrence has the form:

P_{n+1}(x) = (alpha_n * x + beta_n) * P_n(x) + gamma_n * P_{n-1}(x)

Arguments

• properties - Polynomial properties containing recurrence coefficients
• n - Polynomial degree (must be non-negative)
• x - Evaluation point

Returns

Numerical value of P_n(x) computed using recurrence relation

Examples

use mathhook_core::functions::polynomials::evaluation::evaluate_recurrence;
use mathhook_core::functions::polynomials::legendre::LegendreIntelligence;
use mathhook_core::functions::properties::FunctionProperties;

let legendre = LegendreIntelligence::new();
let props = legendre.get_properties();
if let Some(FunctionProperties::Polynomial(legendre_props)) = props.get("legendre_p") {
    let result = evaluate_recurrence(legendre_props, 5, 0.5);
    assert!((result - 0.08984375).abs() < 1e-10);
}