gives the logarithm of the gamma function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- LogGamma[z] is analytic throughout the complex z plane, except for a single branch cut discontinuity along the negative real axis. Log[Gamma[z]] has a more complex branch cut structure.
- For certain special arguments, LogGamma automatically evaluates to exact values.
- LogGamma can be evaluated to arbitrary numerical precision.
- LogGamma automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (4)
Function Properties (8)
LogGamma is defined for all positive real values:
LogGamma is not an analytic function:
LogGamma is neither nondecreasing nor nonincreasing:
LogGamma is not injective:
LogGamma is not surjective:
LogGamma is neither non-negative nor non-positive:
LogGamma is convex on its real domain:
Series Expansions (5)
Taylor expansion for LogGamma around :
Plot the first three approximations for LogGamma around :
Series expansion at poles of the LogGamma function:
LogGamma can be applied to a power series:
Function Identities and Simplifications (3)
Properties & Relations (6)
Use FullSimplify to simplify logarithmic gamma functions:
In TraditionalForm, is automatically interpreted as the gamma function:
Possible Issues (2)
Wolfram Research (1991), LogGamma, Wolfram Language function, https://reference.wolfram.com/language/ref/LogGamma.html.
Wolfram Language. 1991. "LogGamma." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LogGamma.html.
Wolfram Language. (1991). LogGamma. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LogGamma.html