`scipy.special._orthogonal:roots_jacobi`

source: /scipy/special/_orthogonal.py :210

Signature

def roots_jacobi ( n , alpha , beta , mu = False )

Summary

Gauss-Jacobi quadrature.

Extended Summary

Compute the sample points and weights for Gauss-Jacobi quadrature. The sample points are the roots of the nth degree Jacobi polynomial, $P_{n}^{α, β} (x)$ . These sample points and weights correctly integrate polynomials of degree $2 n - 1$ or less over the interval $[- 1, 1]$ with weight function $w (x) = (1 - x)^{α} (1 + x)^{β}$ . See 22.2.1 in [AS] for details.

Parameters

n : int: Quadrature order.
alpha : float: alpha must be > -1
beta : float: beta must be > -1
mu : bool, optional: If True, return the sum of the weights in addition to sample points and weights.

Returns

x : ndarray: Sample points.
w : ndarray: Weights.
mu : float, optional: Sum of the weights, only returned if mu=True.

Examples

from scipy.special import roots_jacobi
x, w = roots_jacobi(3, 0.5, 0.5)

✓

x
w

✗

x, w, mu = roots_jacobi(3, 0.5, 0.5, mu=True)

✓

mu

✗

Aliases

scipy.special.j_roots

Referenced by

This package

release:0.19.0-notes