scipy.special.

roots_sh_chebyt#

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

Gauss-Chebyshev (first kind, shifted) quadrature.

Compute the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth 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 \(w(x) = 1/\sqrt{x - x^2}\). See 22.2.8 in [AS] for more details.

Parameters:

nint: quadrature order
mubool, optional: If True, return the sum of the weights, optional.

Returns:

xndarray: Sample points
wndarray: Weights
mufloat: Sum of the weights