GammaLn

The natural logarithm of , avoiding the overflow of computing Gamma directly for large z.

GammaLn(z), useful where itself would overflow.

Domain: Special functions

Details

Defined via Gamma: for , where is positive so no branch-cut ambiguity arises.
Called gammaln in MATLAB and SciPy, lgamma in C's math library.
Inherits Gamma's recurrence in log form: .
, from .
Diverges to at the nonpositive integers, the poles of Gamma -- the log of a diverging magnitude, rather than the ComplexInfinity that Gamma itself returns there.
It is with a PRINCIPAL logarithm, which for complex is not the same function as Wolfram's : the two differ by multiples of off the positive axis. LogGamma is that continuation, and the one to use where continuity in matters.

Examples