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Fungrim entry: 94db60

∣Γ ⁣(1+yi)∣=πysinh⁡ ⁣(πy)\left|\Gamma\!\left(1 + y i\right)\right| = \sqrt{\frac{\pi y}{\sinh\!\left(\pi y\right)}}
Assumptions:y∈R∖{0}y \in \mathbb{R} \setminus \left\{0\right\}
TeX:
\left|\Gamma\!\left(1 + y i\right)\right| = \sqrt{\frac{\pi y}{\sinh\!\left(\pi y\right)}}

y \in \mathbb{R} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\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("94db60"),
    Formula(Equal(Abs(GammaFunction(Add(1, Mul(y, ConstI)))), Sqrt(Div(Mul(ConstPi, y), Sinh(Mul(ConstPi, y)))))),
    Variables(y),
    Assumptions(Element(y, SetMinus(RR, Set(0)))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC