scipy.special.roots_sh_chebyu#
- scipy.special.roots_sh_chebyu(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 nth degree shifted Chebyshev polynomial of the second kind, \(U_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(w(x) = \sqrt{x - x^2}\). See 22.2.9 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
References
[AS]Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.