Module « scipy.special »

Fonction jv - module scipy.special

Signature de la fonction jv

Description

jv.__doc__

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

jv(v, z)

Bessel function of the first kind of real order and complex argument.

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

Returns
-------
J : ndarray
    Value of the Bessel function, :math:`J_v(z)`.

Notes
-----
For positive `v` values, the computation is carried out using the AMOS
[1]_ `zbesj` routine, which exploits the connection to the modified
Bessel function :math:`I_v`,

.. math::
    J_v(z) = \exp(v\pi\imath/2) I_v(-\imath z)\qquad (\Im z > 0)

    J_v(z) = \exp(-v\pi\imath/2) I_v(\imath z)\qquad (\Im z < 0)

For negative `v` values the formula,

.. math:: J_{-v}(z) = J_v(z) \cos(\pi v) - Y_v(z) \sin(\pi v)

is used, where :math:`Y_v(z)` is the Bessel function of the second
kind, computed using the AMOS routine `zbesy`.  Note that the second
term is exactly zero for integer `v`; to improve accuracy the second
term is explicitly omitted for `v` values such that `v = floor(v)`.

Not to be confused with the spherical Bessel functions (see `spherical_jn`).

See also
--------
jve : :math:`J_v` with leading exponential behavior stripped off.
spherical_jn : spherical Bessel functions.

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