scipy.special.
roots_gegenbauer#
- scipy.special.roots_gegenbauer(n, alpha, mu=False)[source]#
Gauss-Gegenbauer quadrature.
Compute the sample points and weights for Gauss-Gegenbauer quadrature. The sample points are the roots of the nth degree Gegenbauer polynomial, . 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^2)^{\alpha - 1/2}. See 22.2.3 in [AS] for more details.
- Parameters:
- nint
quadrature order
- alphafloat
alpha must be > -0.5
- 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.