`scipy.special._orthogonal:roots_gegenbauer`

source: /scipy/special/_orthogonal.py :1488

Signature

def roots_gegenbauer ( n , alpha , mu = False )

Summary

Gauss-Gegenbauer quadrature.

Extended Summary

Compute the sample points and weights for Gauss-Gegenbauer quadrature. The sample points are the roots of the nth degree Gegenbauer polynomial, $C_{n}^{α} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[- 1, 1]$ with weight function $w (x) = (1 - x^{2})^{α - 1/2}$ . See 22.2.3 in [AS] for more details.

Parameters

n : int: quadrature order
alpha : float: alpha must be > -0.5
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