scipy.special.
roots_chebyu#
- scipy.special.roots_chebyu(n, mu=False)[source]#
- Gauss-Chebyshev (second kind) quadrature. - Computes the sample points and weights for Gauss-Chebyshev quadrature. The sample points are the roots of the nth degree 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 \([-1, 1]\) with weight function \(w(x) = \sqrt{1 - x^2}\). See 22.2.5 in [AS] for 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 
 
 - See also - References [AS]- Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.