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Fungrim entry: dd5e3a

Γ ⁣(x+yi)<Γ ⁣(x+ti)\left|\Gamma\!\left(x + y i\right)\right| < \left|\Gamma\!\left(x + t i\right)\right|
Assumptions:xR  and  yR  and  tR  and  y>tx \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|
\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|
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
GammaΓ(z)\Gamma(z) Gamma function
ConstIii Imaginary unit
RRR\mathbb{R} Real numbers
Source code for this entry:
    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)))))

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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