numpy.polynomial.chebyshev.chebgauss¶
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numpy.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: - 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