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Fonction eval_chebys - module scipy.special

Signature de la fonction eval_chebys

Description

eval_chebys.__doc__

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

eval_chebys(n, x, out=None)

Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a
point.

These polynomials are defined as

.. math::

    S_n(x) = U_n(x/2)

where :math:`U_n` is a Chebyshev polynomial of the second
kind. See 22.5.13 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 Chebyshev polynomial

Returns
-------
S : ndarray
    Values of the Chebyshev polynomial

See Also
--------
roots_chebys : roots and quadrature weights of Chebyshev
               polynomials of the second kind on [-2, 2]
chebys : 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.

Examples
--------
>>> import scipy.special as sc

They are a scaled version of the Chebyshev polynomials of the
second kind.

>>> x = np.linspace(-2, 2, 6)
>>> sc.eval_chebys(3, x)
array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
>>> sc.eval_chebyu(3, x / 2)
array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])