`numpy.polynomial.chebyshev:chebgauss`

source: /numpy/polynomial/chebyshev.py :1791

Signature

def chebgauss ( deg )

Summary

Gauss-Chebyshev quadrature.

Extended Summary

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

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

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 (π (2 i - 1) / (2 n))

w_{i} = π / n

Aliases

numpy.polynomial.chebyshev.chebgauss