scipy.special.la_roots

scipy.special.la_roots(n, alpha, mu=False)

Gauss-generalized Laguerre quadrature.

Computes the sample points and weights for Gauss-generalized Laguerre quadrature. The sample points are the roots of the n-th 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 \(f(x) = x^{\alpha} e^{-x}\).

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

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad