Fungrim home page

Fungrim entry: cc3a51

lim⁡ε→0+[log⁡G ⁣(x+εi)]=log⁡G(x)\lim_{\varepsilon \to {0}^{+}} \left[\log G\!\left(x + \varepsilon i\right)\right] = \log G(x)
Assumptions:x∈R  and⁡  x<0  and⁡  x∉Zx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}
TeX:
\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}
Definitions:
Fungrim symbol Notation Short description
RightLimitlim⁡x→a+f(x)\lim_{x \to {a}^{+}} f(x) Limiting value, from the right
LogBarnesGlog⁡G(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:
Entry(ID("cc3a51"),
    Formula(Equal(RightLimit(Brackets(LogBarnesG(Add(x, Mul(epsilon, ConstI)))), For(epsilon, 0)), LogBarnesG(x))),
    Variables(x),
    Assumptions(And(Element(x, RR), Less(x, 0), NotElement(x, ZZ))))

Topics using this entry

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