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Module « scipy.special »

Fonction ivp - module scipy.special

Signature de la fonction ivp

def ivp(v, z, n=1) 

Description

help(scipy.special.ivp)

Compute derivatives of modified Bessel functions of the first kind.

Compute the nth derivative of the modified Bessel function `Iv`
with respect to `z`.

Parameters
----------
v : array_like or float
    Order of Bessel function
z : array_like
    Argument at which to evaluate the derivative; can be real or
    complex.
n : int, default 1
    Order of derivative. For 0, returns the Bessel function `iv` itself.

Returns
-------
scalar or ndarray
    nth derivative of the modified Bessel function.

See Also
--------
iv

Notes
-----
The derivative is computed using the relation DLFM 10.29.5 [2]_.

References
----------
.. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
       Functions", John Wiley and Sons, 1996, chapter 6.
       https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html

.. [2] NIST Digital Library of Mathematical Functions.
       https://dlmf.nist.gov/10.29.E5

Examples
--------
Compute the modified Bessel function of the first kind of order 0 and
its first two derivatives at 1.

>>> from scipy.special import ivp
>>> ivp(0, 1, 0), ivp(0, 1, 1), ivp(0, 1, 2)
(1.2660658777520084, 0.565159103992485, 0.7009067737595233)

Compute the first derivative of the modified Bessel function of the first
kind for several orders at 1 by providing an array for `v`.

>>> ivp([0, 1, 2], 1, 1)
array([0.5651591 , 0.70090677, 0.29366376])

Compute the first derivative of the modified Bessel function of the
first kind of order 0 at several points by providing an array for `z`.

>>> import numpy as np
>>> points = np.array([0., 1.5, 3.])
>>> ivp(0, points, 1)
array([0.        , 0.98166643, 3.95337022])

Plot the modified Bessel function of the first kind of order 1 and its
first three derivatives.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-5, 5, 1000)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, ivp(1, x, 0), label=r"$I_1$")
>>> ax.plot(x, ivp(1, x, 1), label=r"$I_1'$")
>>> ax.plot(x, ivp(1, x, 2), label=r"$I_1''$")
>>> ax.plot(x, ivp(1, x, 3), label=r"$I_1'''$")
>>> plt.legend()
>>> plt.show()

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