# 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 nth 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.