`scipy.special._orthogonal:roots_genlaguerre`

source: /scipy/special/_orthogonal.py :518

Signature

def roots_genlaguerre ( n , alpha , mu = False )

Summary

Gauss-generalized Laguerre quadrature.

Extended Summary

Compute the sample points and weights for Gauss-generalized Laguerre quadrature. The sample points are the roots of the nth degree generalized Laguerre polynomial, $L_{n}^{α} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[0, \infty]$ with weight function $w (x) = x^{α} e^{- x}$ . See 22.3.9 in [AS] for details.

Parameters

n : int: quadrature order
alpha : float: alpha must be > -1
mu : bool, optional: If True, return the sum of the weights, optional.

Returns

x : ndarray: Sample points
w : ndarray: Weights
mu : float: Sum of the weights

Aliases