# Fungrim entry: 8c96a5

$\log G\!\left(z + 1\right) = \frac{z \left(1 - z\right)}{2} + \frac{z}{2} \log\!\left(2 \pi\right) + z \log \Gamma(z) - \int_{0}^{z} \log \Gamma(x) \, dx$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \left(-\infty, -1\right]$
References:
• https://arxiv.org/abs/math/0308086
TeX:
\log G\!\left(z + 1\right) = \frac{z \left(1 - z\right)}{2} + \frac{z}{2} \log\!\left(2 \pi\right) + z \log \Gamma(z) - \int_{0}^{z} \log \Gamma(x) \, dx

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \left(-\infty, -1\right]
Definitions:
Fungrim symbol Notation Short description
LogBarnesG$\log G(z)$ Logarithmic Barnes G-function
Log$\log(z)$ Natural logarithm
Pi$\pi$ The constant pi (3.14...)
LogGamma$\log \Gamma(z)$ Logarithmic gamma function
Integral$\int_{a}^{b} f(x) \, dx$ Integral
CC$\mathbb{C}$ Complex numbers
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("8c96a5"),
References("https://arxiv.org/abs/math/0308086"))