Module « scipy.special »

Fonction hankel2e - module scipy.special

Signature de la fonction hankel2e

Description

hankel2e.__doc__

hankel2e(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

hankel2e(v, z)

Exponentially scaled Hankel function of the second kind

Defined as::

    hankel2e(v, z) = hankel2(v, z) * exp(1j * z)

Parameters
----------
v : array_like
    Order (float).
z : array_like
    Argument (float or complex).

Returns
-------
out : Values of the exponentially scaled Hankel function of the second kind.

Notes
-----
A wrapper for the AMOS [1]_ routine `zbesh`, which carries out the
computation using the relation,

.. math:: H^{(2)}_v(z) = -\frac{2}{\imath\pi} \exp(\frac{\imath \pi v}{2}) K_v(z exp(\frac{\imath\pi}{2}))

where :math:`K_v` is the modified Bessel function of the second kind.
For negative orders, the relation

.. math:: H^{(2)}_{-v}(z) = H^{(2)}_v(z) \exp(-\imath\pi v)

is used.

References
----------
.. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
       of a Complex Argument and Nonnegative Order",
       http://netlib.org/amos/