# numpy.polynomial.chebyshev.chebgauss#

polynomial.chebyshev.chebgauss(deg)[source]#

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
degint

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

Returns
xndarray

1-D ndarray containing the sample points.

yndarray

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

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