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Fungrim entry: cc3a51

limε0+[logG ⁣(x+εi)]=logG(x)\lim_{\varepsilon \to {0}^{+}} \left[\log G\!\left(x + \varepsilon i\right)\right] = \log G(x)
Assumptions:xR  and  x<0  and  xZx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}
\lim_{\varepsilon \to {0}^{+}} \left[\log G\!\left(x + \varepsilon i\right)\right] = \log G(x)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}
Fungrim symbol Notation Short description
RightLimitlimxa+f(x)\lim_{x \to {a}^{+}} f(x) Limiting value, from the right
LogBarnesGlogG(z)\log G(z) Logarithmic Barnes G-function
ConstIii Imaginary unit
RRR\mathbb{R} Real numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(RightLimit(Brackets(LogBarnesG(Add(x, Mul(epsilon, ConstI)))), For(epsilon, 0)), LogBarnesG(x))),
    Assumptions(And(Element(x, RR), Less(x, 0), NotElement(x, ZZ))))

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2021-03-15 19:12:00.328586 UTC