Module « scipy.special »

Fonction j0 - module scipy.special

Signature de la fonction j0

Description

j0.__doc__

j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

j0(x)

Bessel function of the first kind of order 0.

Parameters
----------
x : array_like
    Argument (float).

Returns
-------
J : ndarray
    Value of the Bessel function of the first kind of order 0 at `x`.

Notes
-----
The domain is divided into the intervals [0, 5] and (5, infinity). In the
first interval the following rational approximation is used:

.. math::

    J_0(x) \approx (w - r_1^2)(w - r_2^2) \frac{P_3(w)}{Q_8(w)},

where :math:`w = x^2` and :math:`r_1`, :math:`r_2` are the zeros of
:math:`J_0`, and :math:`P_3` and :math:`Q_8` are polynomials of degrees 3
and 8, respectively.

In the second interval, the Hankel asymptotic expansion is employed with
two rational functions of degree 6/6 and 7/7.

This function is a wrapper for the Cephes [1]_ routine `j0`.
It should not be confused with the spherical Bessel functions (see
`spherical_jn`).

See also
--------
jv : Bessel function of real order and complex argument.
spherical_jn : spherical Bessel functions.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/