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Fungrim entry: a044e1

Im ⁣(logG(x))=n(n1)2π   where n=x\operatorname{Im}\!\left(\log G(x)\right) = \frac{n \left(n - 1\right)}{2} \pi\; \text{ where } n = \left\lfloor x \right\rfloor
Assumptions:xR  and  x<0  and  xZx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}
\operatorname{Im}\!\left(\log G(x)\right) = \frac{n \left(n - 1\right)}{2} \pi\; \text{ where } n = \left\lfloor x \right\rfloor

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}
Fungrim symbol Notation Short description
ImIm(z)\operatorname{Im}(z) Imaginary part
LogBarnesGlogG(z)\log G(z) Logarithmic Barnes G-function
Piπ\pi The constant pi (3.14...)
RRR\mathbb{R} Real numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(Im(LogBarnesG(x)), Where(Mul(Div(Mul(n, Sub(n, 1)), 2), Pi), Equal(n, Floor(x))))),
    Assumptions(And(Element(x, RR), Less(x, 0), NotElement(x, ZZ))))

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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