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

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.