archimedes.quadrature.gauss_laguerre

archimedes.quadrature.gauss_laguerre(
n: int,
rate: float | None = None,
start: float | None = None,
) → QuadratureRule

Gauss-Laguerre quadrature rule with n nodes.

Nodes are the roots of the degree-n Laguerre polynomial \(L_n(x)\). The rule is exact for polynomials up to degree \(2n - 1\), weighted by the reference weight \(e^{-x}\) on \([0, \infty)\).

Parameters:

  • n (int) – Number of quadrature nodes.

  • rate (float, optional) – Rate/location of the target exponential weight. Default rate=1, start=0.

  • start (float, optional) – Rate/location of the target exponential weight. Default rate=1, start=0.

Returns:

rule – Gauss-Laguerre rule with n nodes on \([0, \infty)\), exact to degree \(2n - 1\), mapped by rate/start if given.

Return type:

QuadratureRule