Module « scipy.special »

Fonction eval_chebyu - module scipy.special

Signature de la fonction eval_chebyu

Description

eval_chebyu.__doc__

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

eval_chebyu(n, x, out=None)

Evaluate Chebyshev polynomial of the second kind at a point.

The Chebyshev polynomials of the second kind can be defined via
the Gauss hypergeometric function :math:`{}_2F_1` as

.. math::

    U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.48 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
-------
U : ndarray
    Values of the Chebyshev polynomial

See Also
--------
roots_chebyu : roots and quadrature weights of Chebyshev
               polynomials of the second kind
chebyu : Chebyshev polynomial object
eval_chebyt : evaluate Chebyshev polynomials of the first kind
hyp2f1 : Gauss hypergeometric function

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.