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# Fungrim entry: dd5e3a

$\left|\Gamma\!\left(x + y i\right)\right| < \left|\Gamma\!\left(x + t i\right)\right|$
Assumptions:$x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; t \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \left|y\right| > \left|t\right|$
TeX:
\left|\Gamma\!\left(x + y i\right)\right| < \left|\Gamma\!\left(x + t i\right)\right|

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; t \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \left|y\right| > \left|t\right|
Definitions:
Fungrim symbol Notation Short description
Abs$\left|z\right|$ Absolute value
Gamma$\Gamma(z)$ Gamma function
ConstI$i$ Imaginary unit
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("dd5e3a"),
Formula(Less(Abs(Gamma(Add(x, Mul(y, ConstI)))), Abs(Gamma(Add(x, Mul(t, ConstI)))))),
Variables(x, y, t),
Assumptions(And(Element(x, RR), Element(y, RR), Element(t, RR), Greater(Abs(y), Abs(t)))))

## 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