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

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

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 ])