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scipy.special.us_roots

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

Gauss-Chebyshev (second 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 second kind, Un(x). These sample points and weights correctly integrate polynomials of degree 2n1 or less over the interval [0,1] with weight function f(x)=xx2.

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

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