scipy.special.eval_chebyc#

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

See also

roots_chebyc: roots and quadrature weights of Chebyshev polynomials of the first kind on [-2, 2]
chebyc: Chebyshev polynomial object
numpy.polynomial.chebyshev.Chebyshev: Chebyshev series
eval_chebyt: evaluate Chebycshev polynomials of the first kind

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.   ])