scipy.special.roots_jacobi¶
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scipy.special.roots_jacobi(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