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Fungrim entry: 774d37

logΓ ⁣(z+1)=logΓ(z)+log(z)\log \Gamma\!\left(z + 1\right) = \log \Gamma(z) + \log(z)
Assumptions:zC{0,1,}z \in \mathbb{C} \setminus \{0, -1, \ldots\}
TeX:
\log \Gamma\!\left(z + 1\right) = \log \Gamma(z) + \log(z)

z \in \mathbb{C} \setminus \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
LogGammalogΓ(z)\log \Gamma(z) Logarithmic gamma function
Loglog(z)\log(z) Natural logarithm
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("774d37"),
    Formula(Equal(LogGamma(Add(z, 1)), Add(LogGamma(z), Log(z)))),
    Variables(z),
    Assumptions(And(Element(z, SetMinus(CC, 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.

2019-10-05 13:11:19.856591 UTC