scipy.special.roots_genlaguerre#

scipy.special.roots_genlaguerre(n, alpha, mu=False)[source]#

Gauss-generalized Laguerre quadrature.

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

Parameters:

nint: quadrature order
alphafloat: alpha must be > -1
mubool, optional: If True, return the sum of the weights, optional.

Returns:

xndarray: Sample points
wndarray: Weights
mufloat: Sum of the weights