scipy.special.roots_jacobi#

scipy.special.roots_jacobi(n, alpha, beta, mu=False)[source]#

Gauss-Jacobi quadrature.

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

Parameters:

nint: quadrature order
alphafloat: alpha must be > -1
betafloat: beta must be > -1
mubool, optional: If True, return the sum of the weights, optional.

Returns:

xndarray: Sample points
wndarray: Weights
mufloat: Sum of the weights