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.