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 
 
 - 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.