scipy.special.roots_sh_chebyt(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 \(f(x) = 1/\sqrt{x - x^2}\).


n : int

quadrature order

mu : bool, optional

If True, return the sum of the weights, optional.


x : ndarray

Sample points

w : ndarray


mu : float

Sum of the weights