scipy.special.gammasgn — SciPy v1.15.2 Manual (original) (raw)
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
the gamma function
log of the absolute value of the gamma function
analytic continuation of the log of the gamma function
Notes
The gamma function can be computed as gammasgn(x) * np.exp(gammaln(x)).
References
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 ])