logGamma — Math

The logarithm of the gamma function of z in Math, is special function.

logGamma(x) = log(Gamma(x))
psi(x) = digamma( x ) — digamma function of a real or complex number

$psi(x) = \psi(x) = digamma(x) = d/dx \; loggamma(x) = \Gamma \; '(x)/ \Gamma(x)$

polygamma(n,x) — polygamma function of a real or complex number

$psi(n,x) = \psi^{(n)}(x) = d^n/dx^n \; \psi(x) = polygamma(n,x) = d^{n+1}/dx^{n+1} \; loggamma(x)$
polygamma(n,x) = zeta(n+1,x) if n>0.
polygamma(-1,x) = psi(-1,x) = logGamma(x)
polygamma(0,x) = digamma( x ) = pis(x) = psi(0,x)

Real part on the real axis:

Imaginary part on the real axis:

Real part on the imaginary axis:

Imaginary part on the imaginary axis:

Real part on the complex plane:

Imaginary part on the complex plane:

Absolute value on the complex plane:

Reference

Related functions: gamma zeta

Function category: gamma functions