scipy.special.s_roots

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

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, \(S_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-2, 2]\) with weight function \(f(x) = \sqrt{1 - (x/2)^2}\).

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