Module « scipy.special »

Fonction hyp1f1 - module scipy.special

Signature de la fonction hyp1f1

Description

hyp1f1.__doc__

hyp1f1(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

hyp1f1(a, b, x, out=None)

Confluent hypergeometric function 1F1.

The confluent hypergeometric function is defined by the series

.. math::

   {}_1F_1(a; b; x) = \sum_{k = 0}^\infty \frac{(a)_k}{(b)_k k!} x^k.

See [dlmf]_ for more details. Here :math:`(\cdot)_k` is the
Pochhammer symbol; see `poch`.

Parameters
----------
a, b : array_like
    Real parameters
x : array_like
    Real or complex argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the confluent hypergeometric function

See also
--------
hyperu : another confluent hypergeometric function
hyp0f1 : confluent hypergeometric limit function
hyp2f1 : Gaussian hypergeometric function

References
----------
.. [dlmf] NIST Digital Library of Mathematical Functions
          https://dlmf.nist.gov/13.2#E2

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

It is one when `x` is zero:

>>> sc.hyp1f1(0.5, 0.5, 0)
1.0

It is singular when `b` is a nonpositive integer.

>>> sc.hyp1f1(0.5, -1, 0)
inf

It is a polynomial when `a` is a nonpositive integer.

>>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0])
>>> sc.hyp1f1(a, b, x)
array([-1., -3., -5., -7.])
>>> 1 + (a / b) * x
array([-1., -3., -5., -7.])

It reduces to the exponential function when `a = b`.

>>> sc.hyp1f1(2, 2, [1, 2, 3, 4])
array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])
>>> np.exp([1, 2, 3, 4])
array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])