numpy.polynomial.chebyshev.chebgauss¶
- polynomial.chebyshev.chebgauss(deg)[source]¶
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
- 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
\[x_i = \cos(\pi (2 i - 1) / (2 n))\]\[w_i = \pi / n\]