5.7.2.11.44. scipy.special.ts_roots¶

scipy.special.ts_roots(n, mu=False)[source]¶

Gauss-Chebyshev (first kind, shifted) quadrature.

Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the n-th degree shifted Chebyshev polynomial of the first kind, $T_n(x)$. These sample points and weights correctly integrate polynomials of degree $2n - 1$ or less over the interval $[0, 1]$ with weight function $f(x) = 1/\sqrt{x - x^2}$.

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

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad