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Fungrim entry: 5261e3

logG ⁣(z+1)=logΓ(z)+logG(z)\log G\!\left(z + 1\right) = \log \Gamma(z) + \log G(z)
Assumptions:zC  and  z{0,1,}z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
\log G\!\left(z + 1\right) = \log \Gamma(z) + \log G(z)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
Fungrim symbol Notation Short description
LogBarnesGlogG(z)\log G(z) Logarithmic Barnes G-function
LogGammalogΓ(z)\log \Gamma(z) Logarithmic gamma function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(LogBarnesG(Add(z, 1)), Add(LogGamma(z), LogBarnesG(z)))),
    Assumptions(And(Element(z, CC), NotElement(z, ZZLessEqual(0)))))

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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