scipy.special.eval_sh_chebyu

scipy.special.eval_sh_chebyu(n, x, out=None) = <ufunc 'eval_sh_chebyu'>

Evaluate shifted Chebyshev polynomial of the second kind at a point.

These polynomials are defined as

\[U_n^*(x) = U_n(2x - 1)\]

where \(U_n\) is a Chebyshev polynomial of the first kind. See 22.5.15 in [AS] for details.

Parameters

narray_like

Degree of the polynomial. If not an integer, the result is determined via the relation to eval_chebyu.

xarray_like

Points at which to evaluate the shifted Chebyshev polynomial

outndarray, optional

Optional output array for the function values

Returns

Uscalar or ndarray

Values of the shifted Chebyshev polynomial

See also

roots_sh_chebyu

roots and quadrature weights of shifted Chebychev polynomials of the second kind

sh_chebyu

shifted Chebyshev polynomial object

eval_chebyu

evaluate Chebyshev polynomials of the second kind

References

AS

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