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Module « scipy.special »

Fonction it2j0y0 - module scipy.special

Signature de la fonction it2j0y0

def it2j0y0(*args, **kwargs) 

Description

help(scipy.special.it2j0y0)

it2j0y0(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    it2j0y0(x, out=None)

    Integrals related to Bessel functions of the first kind of order 0.

    Computes the integrals

    .. math::

        \int_0^x \frac{1 - J_0(t)}{t} dt \\
        \int_x^\infty \frac{Y_0(t)}{t} dt.

    For more on :math:`J_0` and :math:`Y_0` see `j0` and `y0`.

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

    Returns
    -------
    ij0 : scalar or ndarray
        The integral for `j0`
    iy0 : scalar or ndarray
        The integral for `y0`

    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 it2j0y0
    >>> int_j, int_y = it2j0y0(1.)
    >>> int_j, int_y
    (0.12116524699506871, 0.39527290169929336)

    Evaluate the functions at several points.

    >>> import numpy as np
    >>> points = np.array([0.5, 1.5, 3.])
    >>> int_j, int_y = it2j0y0(points)
    >>> int_j, int_y
    (array([0.03100699, 0.26227724, 0.85614669]),
     array([ 0.26968854,  0.29769696, -0.02987272]))

    Plot the functions from 0 to 10.

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(0., 10., 1000)
    >>> int_j, int_y = it2j0y0(x)
    >>> ax.plot(x, int_j, label=r"$\int_0^x \frac{1-J_0(t)}{t}\,dt$")
    >>> ax.plot(x, int_y, label=r"$\int_x^{\infty} \frac{Y_0(t)}{t}\,dt$")
    >>> ax.legend()
    >>> ax.set_ylim(-2.5, 2.5)
    >>> plt.show()
    

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