`scipy.special._orthogonal:roots_sh_chebyt`

source: /scipy/special/_orthogonal.py:2287

Signature

def roots_sh_chebyt(n, mu = False)

Summary

Gauss-Chebyshev (first kind, shifted) quadrature.

Extended Summary

Compute the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth degree shifted Chebyshev polynomial of the first kind, $T_{n} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[0, 1]$ with weight function $w (x) = 1/ x - x^{2}$ . See 22.2.8 in [AS] for more 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