`scipy.special._orthogonal:roots_sh_legendre`

source: /scipy/special/_orthogonal.py :2515

Signature

def roots_sh_legendre ( n , mu = False )

Summary

Gauss-Legendre (shifted) quadrature.

Extended Summary

Compute the sample points and weights for Gauss-Legendre quadrature. The sample points are the roots of the nth degree shifted Legendre polynomial $P_{n}^{*} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[0, 1]$ with weight function $w (x) = 1.0$ . See 2.2.11 in [AS] for details.

Parameters

n : int: quadrature order
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