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. ])