# scipy.special.gammasgn#

scipy.special.gammasgn(x, out=None) = <ufunc 'gammasgn'>#

Sign of the gamma function.

It is defined as

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

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

Parameters:
xarray_like

Real argument

outndarray, optional

Optional output array for the function values

Returns:
scalar or ndarray

Sign of the gamma function

gamma

the gamma function

gammaln

log of the absolute value of the gamma function

loggamma

analytic continuation of the log of the gamma function

Notes

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

References

[dlmf]

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

Examples

>>> import numpy as np
>>> 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 ])