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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:yRy \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
Absz\left|z\right| Absolute value
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
ConstPiπ\pi The constant pi (3.14...)
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("c7b921"),
    Formula(Equal(Abs(GammaFunction(Add(Div(1, 2), Mul(y, ConstI)))), Sqrt(Div(ConstPi, Cosh(Mul(ConstPi, 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.

2019-09-19 20:12:49.583742 UTC