Module « scipy.special »

Fonction ive - module scipy.special

Signature de la fonction ive

Description

ive.__doc__

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

ive(v, z)

Exponentially scaled modified Bessel function of the first kind

Defined as::

    ive(v, z) = iv(v, z) * exp(-abs(z.real))

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

Returns
-------
out : ndarray
    Values of the exponentially scaled modified Bessel function.

Notes
-----
For positive `v`, the AMOS [1]_ `zbesi` routine is called. It uses a
power series for small `z`, the asymptotic expansion for large
`abs(z)`, the Miller algorithm normalized by the Wronskian and a
Neumann series for intermediate magnitudes, and the uniform asymptotic
expansions for :math:`I_v(z)` and :math:`J_v(z)` for large orders.
Backward recurrence is used to generate sequences or reduce orders when
necessary.

The calculations above are done in the right half plane and continued
into the left half plane by the formula,

.. math:: I_v(z \exp(\pm\imath\pi)) = \exp(\pm\pi v) I_v(z)

(valid when the real part of `z` is positive).  For negative `v`, the
formula

.. math:: I_{-v}(z) = I_v(z) + \frac{2}{\pi} \sin(\pi v) K_v(z)

is used, where :math:`K_v(z)` is the modified Bessel function of the
second kind, evaluated using the AMOS routine `zbesk`.

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