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Module « scipy.special »

Fonction i0 - module scipy.special

Signature de la fonction i0

def i0(*args, **kwargs) 

Description

help(scipy.special.i0)

i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    i0(x, out=None)

    Modified Bessel function of order 0.

    Defined as,

    .. math::
        I_0(x) = \sum_{k=0}^\infty \frac{(x^2/4)^k}{(k!)^2} = J_0(\imath x),

    where :math:`J_0` is the Bessel function of the first kind of order 0.

    Parameters
    ----------
    x : array_like
        Argument (float)
    out : ndarray, optional
        Optional output array for the function values

    Returns
    -------
    I : scalar or ndarray
        Value of the modified Bessel function of order 0 at `x`.

    See Also
    --------
    iv: Modified Bessel function of any order
    i0e: Exponentially scaled modified Bessel function of order 0

    Notes
    -----
    The range is partitioned into the two intervals [0, 8] and (8, infinity).
    Chebyshev polynomial expansions are employed in each interval.

    This function is a wrapper for the Cephes [1]_ routine `i0`.

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

    Examples
    --------
    Calculate the function at one point:

    >>> from scipy.special import i0
    >>> i0(1.)
    1.2660658777520082

    Calculate at several points:

    >>> import numpy as np
    >>> i0(np.array([-2., 0., 3.5]))
    array([2.2795853 , 1.        , 7.37820343])

    Plot the function from -10 to 10.

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(-10., 10., 1000)
    >>> y = i0(x)
    >>> ax.plot(x, y)
    >>> plt.show()
    

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