Module « scipy.special »

Fonction kei - module scipy.special

Signature de la fonction kei

Description

kei.__doc__

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

kei(x, out=None)

Kelvin function kei.

Defined as

.. math::

    \mathrm{kei}(x) = \Im[K_0(x e^{\pi i / 4})]

where :math:`K_0` is the modified Bessel function of the second
kind (see `kv`). See [dlmf]_ for more details.

Parameters
----------
x : array_like
    Real argument.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    Values of the Kelvin function.

See Also
--------
ker : the corresponding real part
keip : the derivative of kei
kv : modified Bessel function of the second kind

References
----------
.. [dlmf] NIST, Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/10.61

Examples
--------
It can be expressed using the modified Bessel function of the
second kind.

>>> import scipy.special as sc
>>> x = np.array([1.0, 2.0, 3.0, 4.0])
>>> sc.kv(0, x * np.exp(np.pi * 1j / 4)).imag
array([-0.49499464, -0.20240007, -0.05112188,  0.0021984 ])
>>> sc.kei(x)
array([-0.49499464, -0.20240007, -0.05112188,  0.0021984 ])