scipy.special.eval_chebyc — SciPy v1.15.2 Manual (original) (raw)

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

Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a point.

These polynomials are defined as

\[C_n(x) = 2 T_n(x/2)\]

where \(T_n\) is a Chebyshev polynomial of the first kind. See 22.5.11 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 Chebyshev polynomial

outndarray, optional

Optional output array for the function values

Returns:

Cscalar or ndarray

Values of the Chebyshev polynomial

References

[AS]

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

Examples

import numpy as np import scipy.special as sc

They are a scaled version of the Chebyshev polynomials of the first kind.

x = np.linspace(-2, 2, 6) sc.eval_chebyc(3, x) array([-2. , 1.872, 1.136, -1.136, -1.872, 2. ]) 2 * sc.eval_chebyt(3, x / 2) array([-2. , 1.872, 1.136, -1.136, -1.872, 2. ])