Fungrim entry: 86b3ec

G\!\left(z + 1\right) = \Gamma(z) G(z)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

TeX:

G\!\left(z + 1\right) = \Gamma(z) G(z)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`BarnesG`	$G(z)$	Barnes G-function
`Gamma`	$\Gamma(z)$	Gamma function
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("86b3ec"),
    Formula(Equal(BarnesG(Add(z, 1)), Mul(Gamma(z), BarnesG(z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(0)))))

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