scipy.special.eval_sh_chebyt

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

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

These polynomials are defined as

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

where \(T_n\) is a Chebyshev polynomial of the first kind. See 22.5.14 in [AS] for details.

Parameters:

narray_like

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

xarray_like

Points at which to evaluate the shifted Chebyshev polynomial

outndarray, optional

Optional output array for the function values

Returns:

Tscalar or ndarray

Values of the shifted Chebyshev polynomial

See also

roots_sh_chebyt

roots and quadrature weights of shifted Chebyshev polynomials of the first kind

sh_chebyt

shifted Chebyshev polynomial object

eval_chebyt

evaluate Chebyshev polynomials of the first kind

numpy.polynomial.chebyshev.Chebyshev

Chebyshev series

References

[AS]

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