`scipy.special._orthogonal:roots_sh_jacobi`

source: /scipy/special/_orthogonal.py:408

Signature

def roots_sh_jacobi(n, p1, q1, mu = False)

Summary

Gauss-Jacobi (shifted) quadrature.

Extended Summary

Compute the sample points and weights for Gauss-Jacobi (shifted) quadrature. The sample points are the roots of the nth degree shifted Jacobi polynomial, $G_{n}^{p, q} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[0, 1]$ with weight function $w (x) = (1 - x)^{p - q} x^{q - 1}$ . See 22.2.2 in [AS] for details.

Parameters

n : int: quadrature order.
p1 : float: (p1 - q1) must be > -1.
q1 : float: q1 must be > 0.
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