# scipy.special.chebys

scipy.special.chebys(n, monic=False)

  Chebyshev polynomial of the second kind on \([-2, 2]\).

  Defined as \(S_n(x) = U_n(x/2)\) where \(U_n\) is the nth Chebychev polynomial of the second kind.

  Parameters:
    n int

      Degree of the polynomial.

    monic bool, optional

      If True, scale the leading coefficient to be 1. Default is False.

  Returns:
    S orthopoly1d

      Chebyshev polynomial of the second kind on \([-2, 2]\).

  See also

  `chebyu`

    Chebyshev polynomial of the second kind

  Notes

  The polynomials \(S_n(x)\) are orthogonal over \([-2, 2]\) with weight function \(\sqrt{1 - (x/2)}^2\).

  References

  [1]

  Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.