`scipy.special._orthogonal:roots_chebyu`

source: /scipy/special/_orthogonal.py :1811

Signature

def roots_chebyu ( n , mu = False )

Summary

Gauss-Chebyshev (second kind) quadrature.

Extended Summary

Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth degree Chebyshev polynomial of the second kind, $U_{n} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[- 1, 1]$ with weight function $w (x) = 1 - x^{2}$ . See 22.2.5 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