scipy.special.eval_chebyt#
- scipy.special.eval_chebyt(n, x, out=None) = <ufunc 'eval_chebyt'>#
- Evaluate Chebyshev polynomial of the first kind at a point. - The Chebyshev polynomials of the first kind can be defined via the Gauss hypergeometric function \({}_2F_1\) as \[T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).\]- When \(n\) is an integer the result is a polynomial of degree \(n\). See 22.5.47 in [AS] for details. - Parameters:
- narray_like
- Degree of the polynomial. If not an integer, the result is determined via the relation to the Gauss hypergeometric function. 
- xarray_like
- Points at which to evaluate the Chebyshev polynomial 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- Tscalar or ndarray
- Values of the Chebyshev polynomial 
 
 - See also - roots_chebyt
- roots and quadrature weights of Chebyshev polynomials of the first kind 
- chebyu
- Chebychev polynomial object 
- eval_chebyu
- evaluate Chebyshev polynomials of the second kind 
- hyp2f1
- Gauss hypergeometric function 
- numpy.polynomial.chebyshev.Chebyshev
- Chebyshev series 
 - Notes - This routine is numerically stable for x in - [-1, 1]at least up to order- 10000.- References [AS]- Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.