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Module « scipy.special »

Fonction it2i0k0 - module scipy.special

Signature de la fonction it2i0k0

def it2i0k0(*args, **kwargs) 

Description

help(scipy.special.it2i0k0)

it2i0k0(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    it2i0k0(x, out=None)

    Integrals related to modified Bessel functions of order 0.

    Computes the integrals

    .. math::

        \int_0^x \frac{I_0(t) - 1}{t} dt \\
        \int_x^\infty \frac{K_0(t)}{t} dt.

    Parameters
    ----------
    x : array_like
        Values at which to evaluate the integrals.
    out : tuple of ndarrays, optional
        Optional output arrays for the function results.

    Returns
    -------
    ii0 : scalar or ndarray
        The integral for `i0`
    ik0 : scalar or ndarray
        The integral for `k0`

    References
    ----------
    .. [1] S. Zhang and J.M. Jin, "Computation of Special Functions",
           Wiley 1996

    Examples
    --------
    Evaluate the functions at one point.

    >>> from scipy.special import it2i0k0
    >>> int_i, int_k = it2i0k0(1.)
    >>> int_i, int_k
    (0.12897944249456852, 0.2085182909001295)

    Evaluate the functions at several points.

    >>> import numpy as np
    >>> points = np.array([0.5, 1.5, 3.])
    >>> int_i, int_k = it2i0k0(points)
    >>> int_i, int_k
    (array([0.03149527, 0.30187149, 1.50012461]),
     array([0.66575102, 0.0823715 , 0.00823631]))

    Plot the functions from 0 to 5.

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(0., 5., 1000)
    >>> int_i, int_k = it2i0k0(x)
    >>> ax.plot(x, int_i, label=r"$\int_0^x \frac{I_0(t)-1}{t}\,dt$")
    >>> ax.plot(x, int_k, label=r"$\int_x^{\infty} \frac{K_0(t)}{t}\,dt$")
    >>> ax.legend()
    >>> ax.set_ylim(0, 10)
    >>> plt.show()
    

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