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
See also
References
[AS]Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.