Module « scipy.special »

Fonction kn - module scipy.special

Signature de la fonction kn

Description

kn.__doc__

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

kn(n, x)

Modified Bessel function of the second kind of integer order `n`

Returns the modified Bessel function of the second kind for integer order
`n` at real `z`.

These are also sometimes called functions of the third kind, Basset
functions, or Macdonald functions.

Parameters
----------
n : array_like of int
    Order of Bessel functions (floats will truncate with a warning)
z : array_like of float
    Argument at which to evaluate the Bessel functions

Returns
-------
out : ndarray
    The results

Notes
-----
Wrapper for AMOS [1]_ routine `zbesk`.  For a discussion of the
algorithm used, see [2]_ and the references therein.

See Also
--------
kv : Same function, but accepts real order and complex argument
kvp : Derivative of this function

References
----------
.. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
       of a Complex Argument and Nonnegative Order",
       http://netlib.org/amos/
.. [2] Donald E. Amos, "Algorithm 644: A portable package for Bessel
       functions of a complex argument and nonnegative order", ACM
       TOMS Vol. 12 Issue 3, Sept. 1986, p. 265

Examples
--------
Plot the function of several orders for real input:

>>> from scipy.special import kn
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0, 5, 1000)
>>> for N in range(6):
...     plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N))
>>> plt.ylim(0, 10)
>>> plt.legend()
>>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$')
>>> plt.show()

Calculate for a single value at multiple orders:

>>> kn([4, 5, 6], 1)
array([   44.23241585,   360.9605896 ,  3653.83831186])