Module « scipy.special »

Fonction hyperu - module scipy.special

Signature de la fonction hyperu

Description

hyperu.__doc__

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

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

Confluent hypergeometric function U

It is defined as the solution to the equation

.. math::

   x \frac{d^2w}{dx^2} + (b - x) \frac{dw}{dx} - aw = 0

which satisfies the property

.. math::

   U(a, b, x) \sim x^{-a}

as :math:`x \to \infty`. See [dlmf]_ for more details.

Parameters
----------
a, b : array_like
    Real-valued parameters
x : array_like
    Real-valued argument
out : ndarray
    Optional output array for the function values

Returns
-------
scalar or ndarray
    Values of `U`

References
----------
.. [dlmf] NIST Digital Library of Mathematics Functions
          https://dlmf.nist.gov/13.2#E6

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

It has a branch cut along the negative `x` axis.

>>> x = np.linspace(-0.1, -10, 5)
>>> sc.hyperu(1, 1, x)
array([nan, nan, nan, nan, nan])

It approaches zero as `x` goes to infinity.

>>> x = np.array([1, 10, 100])
>>> sc.hyperu(1, 1, x)
array([0.59634736, 0.09156333, 0.00990194])

It satisfies Kummer's transformation.

>>> a, b, x = 2, 1, 1
>>> sc.hyperu(a, b, x)
0.1926947246463881
>>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x)
0.1926947246463881