scipy.special.roots_sh_chebyu

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

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, \(U_n(x)\). 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

See also

scipy.integrate.quadrature

scipy.integrate.fixed_quad

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.