scipy.special.roots_gegenbauer¶
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scipy.special.
roots_gegenbauer
(n, alpha, mu=False)[source]¶ Gauss-Gegenbauer quadrature.
Computes the sample points and weights for Gauss-Gegenbauer quadrature. The sample points are the roots of the n-th degree Gegenbauer polynomial, \(C^{\alpha}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-1, 1]\) with weight function \(f(x) = (1 - x^2)^{\alpha - 1/2}\).
- 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