Module « scipy.special »

Fonction expn - module scipy.special

Signature de la fonction expn

Description

expn.__doc__

expn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

expn(n, x, out=None)

Generalized exponential integral En.

For integer :math:`n \geq 0` and real :math:`x \geq 0` the
generalized exponential integral is defined as [dlmf]_

.. math::

    E_n(x) = x^{n - 1} \int_x^\infty \frac{e^{-t}}{t^n} dt.

Parameters
----------
n: array_like
    Non-negative integers
x: array_like
    Real argument
out: ndarray, optional
    Optional output array for the function results

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

See Also
--------
exp1 : special case of :math:`E_n` for :math:`n = 1`
expi : related to :math:`E_n` when :math:`n = 1`

References
----------
.. [dlmf] Digital Library of Mathematical Functions, 8.19.2
          https://dlmf.nist.gov/8.19#E2

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

Its domain is nonnegative n and x.

>>> sc.expn(-1, 1.0), sc.expn(1, -1.0)
(nan, nan)

It has a pole at ``x = 0`` for ``n = 1, 2``; for larger ``n`` it
is equal to ``1 / (n - 1)``.

>>> sc.expn([0, 1, 2, 3, 4], 0)
array([       inf,        inf, 1.        , 0.5       , 0.33333333])

For n equal to 0 it reduces to ``exp(-x) / x``.

>>> x = np.array([1, 2, 3, 4])
>>> sc.expn(0, x)
array([0.36787944, 0.06766764, 0.01659569, 0.00457891])
>>> np.exp(-x) / x
array([0.36787944, 0.06766764, 0.01659569, 0.00457891])

For n equal to 1 it reduces to `exp1`.

>>> sc.expn(1, x)
array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
>>> sc.exp1(x)
array([0.21938393, 0.04890051, 0.01304838, 0.00377935])