scipy.special.roots_sh_jacobi#
- scipy.special.roots_sh_jacobi(n, p1, q1, mu=False)[source]#
Gauss-Jacobi (shifted) quadrature.
Compute the sample points and weights for Gauss-Jacobi (shifted) quadrature. The sample points are the roots of the nth degree shifted Jacobi polynomial, \(G^{p,q}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(w(x) = (1 - x)^{p-q} x^{q-1}\). See 22.2.2 in [AS] for details.
- Parameters:
- nint
quadrature order
- p1float
(p1 - q1) must be > -1
- q1float
q1 must be > 0
- mubool, optional
If True, return the sum of the weights, optional.
- Returns:
- xndarray
Sample points
- wndarray
Weights
- mufloat
Sum of the weights
References
[AS]Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.