/**
 * Gauss-Legendre quadrature nodes and weights.
 *
 * `rootsLegendre(n)` finds the n roots of the degree-n Legendre polynomial
 * P_n via Newton's method (initial guess from the standard asymptotic
 * approximation), then derives the corresponding quadrature weights. This is
 * the classical fixed-node table underlying Gauss-Legendre quadrature on
 * [-1, 1]; callers needing a custom node count (rather than the library's
 * built-in fixed-order `integrate`/`gaussLegendre` routines) use this
 * directly.
 *
 * @packageDocumentation
 */
/** Result of {@link rootsLegendre}: nodes ascending on [-1, 1] with matching weights. */
export interface RootsLegendreResult {
    nodes: number[];
    weights: number[];
}
/**
 * n-point Gauss-Legendre quadrature nodes and weights on [-1, 1].
 *
 * Nodes are the roots of the degree-n Legendre polynomial P_n, refined by
 * Newton's method from the standard asymptotic initial guess
 * `cos(pi*(i+0.75)/(n+0.5))`. Weights are `2 / ((1-x_i^2) * P'_n(x_i)^2)`.
 *
 * @param n - Number of quadrature points (positive integer)
 * @returns Nodes (ascending) and matching weights
 *
 * @example
 * rootsLegendre(3)
 * // { nodes: [-0.7745966692, 0, 0.7745966692],
 * //   weights: [0.5555555556, 0.8888888889, 0.5555555556] }
 */
export declare function rootsLegendre(n: number): RootsLegendreResult;
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