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Fonction eval_sh_chebyu - module scipy.special

Signature de la fonction eval_sh_chebyu

Description

eval_sh_chebyu.__doc__

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

eval_sh_chebyu(n, x, out=None)

Evaluate shifted Chebyshev polynomial of the second kind at a
point.

These polynomials are defined as

.. math::

    U_n^*(x) = U_n(2x - 1)

where :math:`U_n` is a Chebyshev polynomial of the first kind. See
22.5.15 in [AS]_ for details.

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

Returns
-------
U : ndarray
    Values of the shifted Chebyshev polynomial

See Also
--------
roots_sh_chebyu : roots and quadrature weights of shifted
                  Chebychev polynomials of the second kind
sh_chebyu : shifted Chebyshev polynomial object
eval_chebyu : evaluate Chebyshev polynomials of the second kind

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