5.7.2.11.36. scipy.special.j_roots¶

scipy.special.j_roots(n, alpha, beta, mu=False)[source]¶

Gauss-Jacobi quadrature.

Computes the sample points and weights for Gauss-Jacobi quadrature. The sample points are the roots of the n-th 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 $f(x) = (1 - x)^{\alpha} (1 + x)^{\beta}$.

Parameters:	n : int quadrature order alpha : float alpha must be > -1 beta : float beta 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

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad