# Fungrim entry: 4a3612

$\log G\!\left(x + 1\right) < \left(\frac{{x}^{2}}{2} - \frac{1}{12}\right) \log(x) - \frac{3 {x}^{2}}{4} + \frac{\log\!\left(2 \pi\right)}{2} x + \frac{1}{12} - \log(A)$
Assumptions:$x \in \left(0, \infty\right)$
References:
• https://dx.doi.org/10.1098/rspa.2014.0534
TeX:
\log G\!\left(x + 1\right) < \left(\frac{{x}^{2}}{2} - \frac{1}{12}\right) \log(x) - \frac{3 {x}^{2}}{4} + \frac{\log\!\left(2 \pi\right)}{2} x + \frac{1}{12} - \log(A)

x \in \left(0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
LogBarnesG$\log G(z)$ Logarithmic Barnes G-function
Pow${a}^{b}$ Power
Log$\log(z)$ Natural logarithm
Pi$\pi$ The constant pi (3.14...)
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("4a3612"),
Formula(Less(LogBarnesG(Add(x, 1)), Sub(Add(Add(Sub(Mul(Sub(Div(Pow(x, 2), 2), Div(1, 12)), Log(x)), Div(Mul(3, Pow(x, 2)), 4)), Mul(Div(Log(Mul(2, Pi)), 2), x)), Div(1, 12)), Log(ConstGlaisher)))),
Variables(x),
Assumptions(Element(x, OpenInterval(0, Infinity))),
References("https://dx.doi.org/10.1098/rspa.2014.0534"))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC