scipy.special.

roots_chebys#

scipy.special.roots_chebys(n, mu=False)[source]#

Gauss-Chebyshev (second kind) quadrature.

Compute the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth degree Chebyshev polynomial of the second kind, \(S_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-2, 2]\) with weight function \(w(x) = \sqrt{1 - (x/2)^2}\). See 22.2.7 in [AS] for more details.

Parameters:

nint: quadrature order
mubool, optional: If True, return the sum of the weights, optional.

Returns:

xndarray: Sample points
wndarray: Weights
mufloat: Sum of the weights