Module « scipy.special »

Fonction yv - module scipy.special

Signature de la fonction yv

Description

yv.__doc__

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

yv(v, z)

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

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

Returns
-------
Y : ndarray
    Value of the Bessel function of the second kind, :math:`Y_v(x)`.

Notes
-----
For positive `v` values, the computation is carried out using the
AMOS [1]_ `zbesy` routine, which exploits the connection to the Hankel
Bessel functions :math:`H_v^{(1)}` and :math:`H_v^{(2)}`,

.. math:: Y_v(z) = \frac{1}{2\imath} (H_v^{(1)} - H_v^{(2)}).

For negative `v` values the formula,

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

is used, where :math:`J_v(z)` is the Bessel function of the first kind,
computed using the AMOS routine `zbesj`.  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)`.

See also
--------
yve : :math:`Y_v` with leading exponential behavior stripped off.

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