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# 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

  [R391] | Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.