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. ])