scipy.special.

roots_gegenbauer

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

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, \(C^{\alpha}_n(x)\). 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

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

scipy.integrate.quadrature

scipy.integrate.fixed_quad

References

[AS]

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