scipy.special.gammaln#
- scipy.special.gammaln(x, out=None) = <ufunc 'gammaln'>#
Logarithm of the absolute value of the gamma function.
Defined as
\[\ln(\lvert\Gamma(x)\rvert)\]where \(\Gamma\) is the gamma function. For more details on the gamma function, see [dlmf].
- Parameters
- xarray_like
Real argument
- outndarray, optional
Optional output array for the function results
- Returns
- scalar or ndarray
Values of the log of the absolute value of gamma
See also
Notes
It is the same function as the Python standard library function
math.lgamma
.When used in conjunction with
gammasgn
, this function is useful for working in logspace on the real axis without having to deal with complex numbers via the relationexp(gammaln(x)) = gammasgn(x) * gamma(x)
.For complex-valued log-gamma, use
loggamma
instead ofgammaln
.References
- dlmf
NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/5
Examples
>>> import scipy.special as sc
It has two positive zeros.
>>> sc.gammaln([1, 2]) array([0., 0.])
It has poles at nonpositive integers.
>>> sc.gammaln([0, -1, -2, -3, -4]) array([inf, inf, inf, inf, inf])
It asymptotically approaches
x * log(x)
(Stirling’s formula).>>> x = np.array([1e10, 1e20, 1e40, 1e80]) >>> sc.gammaln(x) array([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82]) >>> x * np.log(x) array([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])