Module « scipy.special »

Fonction hankel1e - module scipy.special

Signature de la fonction hankel1e

Description

hankel1e.__doc__

hankel1e(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

hankel1e(v, z)

Exponentially scaled Hankel function of the first kind

Defined as::

    hankel1e(v, z) = hankel1(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.

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

.. math:: H^{(1)}_v(z) = \frac{2}{\imath\pi} \exp(-\imath \pi v/2) K_v(z \exp(-\imath\pi/2))

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

.. math:: H^{(1)}_{-v}(z) = H^{(1)}_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/