maxframe.tensor.special.gammasgn

maxframe.tensor.special.gammasgn(x, out=None)

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:

• x (array_like) – Real argument

• out (ndarray, optional) – Optional output array for the function values

Returns:

Sign of the gamma function

Return type:

scalar or ndarray

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