# scipy.special.roots_chebyt

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

  Gauss-Chebyshev (first 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 first kind, \(T_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-1, 1]\) with weight function \(w(x) = 1/\sqrt{1 - x^2}\). See 22.2.4 in [AS] for more details.

  Parameters
    n int

      quadrature order

    mu bool, optional

      If True, return the sum of the weights, optional.

  Returns
    x ndarray

      Sample points

    w ndarray

      Weights

    mu float

      Sum of the weights

  See also

  `scipy.integrate.quadrature`
  `scipy.integrate.fixed_quad`
  `numpy.polynomial.chebyshev.chebgauss`

  References

  AS

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

scipy.special.roots_legendre scipy.special.roots_chebyu