Module « scipy.special »

Fonction eval_chebyc - module scipy.special

Signature de la fonction eval_chebyc

Description

eval_chebyc.__doc__

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

eval_chebyc(n, x, out=None)

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

These polynomials are defined as

.. math::

    C_n(x) = 2 T_n(x/2)

where :math:`T_n` is a Chebyshev polynomial of the first kind. See
22.5.11 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_chebyt`.
x : array_like
    Points at which to evaluate the Chebyshev polynomial

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

See Also
--------
roots_chebyc : roots and quadrature weights of Chebyshev
               polynomials of the first kind on [-2, 2]
chebyc : Chebyshev polynomial object
numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
eval_chebyt : evaluate Chebycshev polynomials of the first 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
first kind.

>>> x = np.linspace(-2, 2, 6)
>>> sc.eval_chebyc(3, x)
array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])
>>> 2 * sc.eval_chebyt(3, x / 2)
array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])