Module « scipy.special »

Fonction iv - module scipy.special

Signature de la fonction iv

Description

iv.__doc__

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

iv(v, z)

Modified Bessel function of the first kind of real order.

Parameters
----------
v : array_like
    Order. If `z` is of real type and negative, `v` must be integer
    valued.
z : array_like of float or complex
    Argument.

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

Notes
-----
For real `z` and :math:`v \in [-50, 50]`, the evaluation is carried out
using Temme's method [1]_.  For larger orders, uniform asymptotic
expansions are applied.

For complex `z` and positive `v`, the AMOS [2]_ `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`.

See also
--------
kve : This function with leading exponential behavior stripped off.

References
----------
.. [1] Temme, Journal of Computational Physics, vol 21, 343 (1976)
.. [2] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
       of a Complex Argument and Nonnegative Order",
       http://netlib.org/amos/