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Fungrim entry: c7b921

∣Γ ⁣(12+yi)∣=πcosh⁡ ⁣(πy)\left|\Gamma\!\left(\frac{1}{2} + y i\right)\right| = \sqrt{\frac{\pi}{\cosh\!\left(\pi y\right)}}
Assumptions:y∈Ry \in \mathbb{R}
TeX:
\left|\Gamma\!\left(\frac{1}{2} + y i\right)\right| = \sqrt{\frac{\pi}{\cosh\!\left(\pi y\right)}}

y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
GammaΓ(z)\Gamma(z) Gamma function
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("c7b921"),
    Formula(Equal(Abs(Gamma(Add(Div(1, 2), Mul(y, ConstI)))), Sqrt(Div(Pi, Cosh(Mul(Pi, y)))))),
    Variables(y),
    Assumptions(Element(y, RR)))

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