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Fungrim entry: f3b870

logΓ(z)=ζ ⁣(0,z)+log ⁣(2π)2\log \Gamma(z) = \zeta'\!\left(0, z\right) + \frac{\log\!\left(2 \pi\right)}{2}
Assumptions:zC{0,1,}z \in \mathbb{C} \setminus \{0, -1, \ldots\}
\log \Gamma(z) = \zeta'\!\left(0, z\right) + \frac{\log\!\left(2 \pi\right)}{2}

z \in \mathbb{C} \setminus \{0, -1, \ldots\}
Fungrim symbol Notation Short description
LogGammalogΓ(z)\log \Gamma(z) Logarithmic gamma function
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Loglog(z)\log(z) Natural logarithm
Piπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(LogGamma(z), Add(HurwitzZeta(0, z, 1), Div(Log(Mul(2, Pi)), 2)))),
    Assumptions(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.

2021-03-15 19:12:00.328586 UTC