numpy.polynomial.chebyshev.chebgauss

numpy.polynomial.chebyshev.chebgauss(deg)

Gauss-Chebyshev quadrature.

Computes the sample points and weights for Gauss-Chebyshev quadrature. These sample points and weights will correctly integrate polynomials of degree 2*deg - 1 or less over the interval [-1, 1] with the weight function f(x) = 1/\sqrt{1 - x^2}.

Parameters:

deg : int

Number of sample points and weights. It must be >= 1.

Returns:

x : ndarray

1-D ndarray containing the sample points.

y : ndarray

1-D ndarray containing the weights.

Notes

New in version 1.7.0.

The results have only been tested up to degree 100, higher degrees may be problematic. For Gauss-Chebyshev there are closed form solutions for the sample points and weights. If n = deg, then

x_i = \cos(\pi (2 i - 1) / (2 n))

w_i = \pi / n