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Module « scipy.special »

Fonction exp1 - module scipy.special

Signature de la fonction exp1

def exp1(*args, **kwargs) 

Description

help(scipy.special.exp1)

exp1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    exp1(z, out=None)

    Exponential integral E1.

    For complex :math:`z \ne 0` the exponential integral can be defined as
    [1]_

    .. math::

       E_1(z) = \int_z^\infty \frac{e^{-t}}{t} dt,

    where the path of the integral does not cross the negative real
    axis or pass through the origin.

    Parameters
    ----------
    z: array_like
        Real or complex argument.
    out : ndarray, optional
        Optional output array for the function results

    Returns
    -------
    scalar or ndarray
        Values of the exponential integral E1

    See Also
    --------
    expi : exponential integral :math:`Ei`
    expn : generalization of :math:`E_1`

    Notes
    -----
    For :math:`x > 0` it is related to the exponential integral
    :math:`Ei` (see `expi`) via the relation

    .. math::

       E_1(x) = -Ei(-x).

    References
    ----------
    .. [1] Digital Library of Mathematical Functions, 6.2.1
           https://dlmf.nist.gov/6.2#E1

    Examples
    --------
    >>> import numpy as np
    >>> import scipy.special as sc

    It has a pole at 0.

    >>> sc.exp1(0)
    inf

    It has a branch cut on the negative real axis.

    >>> sc.exp1(-1)
    nan
    >>> sc.exp1(complex(-1, 0))
    (-1.8951178163559368-3.141592653589793j)
    >>> sc.exp1(complex(-1, -0.0))
    (-1.8951178163559368+3.141592653589793j)

    It approaches 0 along the positive real axis.

    >>> sc.exp1([1, 10, 100, 1000])
    array([2.19383934e-01, 4.15696893e-06, 3.68359776e-46, 0.00000000e+00])

    It is related to `expi`.

    >>> x = np.array([1, 2, 3, 4])
    >>> sc.exp1(x)
    array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
    >>> -sc.expi(-x)
    array([0.21938393, 0.04890051, 0.01304838, 0.00377935])

    

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