# scipy.special.roots_gegenbauer¶

scipy.special.roots_gegenbauer(n, alpha, mu=False)[source]

Compute 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 $$w(x) = (1 - x^2)^{\alpha - 1/2}$$. See 22.2.3 in [AS] for more details.

Parameters
nint

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

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.

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