Fungrim entry: daef08

\log G(n) = \begin{cases} \log\!\left(G(n)\right), & n \ge 1\\-\infty, & n \le 0\\ \end{cases}

Assumptions:

n \in \mathbb{Z}

TeX:

\log G(n) = \begin{cases} \log\!\left(G(n)\right), & n \ge 1\\-\infty, & n \le 0\\ \end{cases}

n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`LogBarnesG`	$\log G(z)$	Logarithmic Barnes G-function
`Log`	$\log(z)$	Natural logarithm
`BarnesG`	$G(z)$	Barnes G-function
`Infinity`	$\infty$	Positive infinity
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("daef08"),
    Formula(Equal(LogBarnesG(n), Cases(Tuple(Log(BarnesG(n)), GreaterEqual(n, 1)), Tuple(Neg(Infinity), LessEqual(n, 0))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

Topics using this entry

Barnes G-function

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