scipy.special.u_roots¶
- scipy.special.u_roots(n, mu=False)[source]¶
Gauss-Chebyshev (second kind) quadrature.
Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the n-th degree Chebyshev polynomial of the second kind, \(U_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-1, 1]\) with weight function \(f(x) = \sqrt{1 - x^2}\).
Parameters: n : int
quadrature order
mu : bool, optional
If True, return the sum of the weights, optional.
Returns: x : ndarray
Sample points
w : ndarray
Weights
mu : float
Sum of the weights