scipy.special.gammasgn¶
-
scipy.special.gammasgn(x) = <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
- Returns
- scalar or ndarray
Sign of the gamma function
See also
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 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 ])