Module « scipy.special »

Fonction gammasgn - module scipy.special

Signature de la fonction gammasgn

Description

gammasgn.__doc__

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

gammasgn(x)

Sign of the gamma function.

It is defined as

.. math::

   \text{gammasgn}(x) =
   \begin{cases}
     +1 & \Gamma(x) > 0 \\
     -1 & \Gamma(x) < 0
   \end{cases}

where :math:`\Gamma` is the gamma function; see `gamma`. This
definition is complete since the gamma function is never zero;
see the discussion after [dlmf]_.

Parameters
----------
x : array_like
    Real argument

Returns
-------
scalar or ndarray
    Sign of the gamma function

Notes
-----
The gamma function can be computed as ``gammasgn(x) *
np.exp(gammaln(x))``.

See Also
--------
gamma : the gamma function
gammaln : log of the absolute value of the gamma function
loggamma : analytic continuation of the log of the gamma function

References
----------
.. [dlmf] NIST Digital Library of Mathematical Functions
          https://dlmf.nist.gov/5.2#E1

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

It is 1 for `x > 0`.

>>> sc.gammasgn([1, 2, 3, 4])
array([1., 1., 1., 1.])

It alternates between -1 and 1 for negative integers.

>>> sc.gammasgn([-0.5, -1.5, -2.5, -3.5])
array([-1.,  1., -1.,  1.])

It can be used to compute the gamma function.

>>> x = [1.5, 0.5, -0.5, -1.5]
>>> sc.gammasgn(x) * np.exp(sc.gammaln(x))
array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])
>>> sc.gamma(x)
array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])