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Fonction eval_chebyt - module scipy.special

Signature de la fonction eval_chebyt

Description

eval_chebyt.__doc__

eval_chebyt(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

eval_chebyt(n, x, out=None)

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 :math:`{}_2F_1` as

.. math::

    T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.47 in [AS]_ for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the Gauss hypergeometric
    function.
x : array_like
    Points at which to evaluate the Chebyshev polynomial

Returns
-------
T : 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.