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.