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.