scipy.special.ts_roots

scipy.special.ts_roots(n, mu=False)

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