# scipy.special.roots_genlaguerre#

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

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

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

References

[AS]

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.