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.