scipy.special.gammaln(x, out=None) = <ufunc 'gammaln'>#

Logarithm of the absolute value of the gamma function.

Defined as


where \(\Gamma\) is the gamma function. For more details on the gamma function, see [dlmf].


Real argument

outndarray, optional

Optional output array for the function results

scalar or ndarray

Values of the log of the absolute value of gamma

See also


sign of the gamma function


principal branch of the logarithm of the gamma function


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 relation exp(gammaln(x)) = gammasgn(x) * gamma(x).

For complex-valued log-gamma, use loggamma instead of gammaln.



NIST Digital Library of Mathematical Functions


>>> import numpy as np
>>> 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])