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Fungrim entry: 1976db

Γ ⁣(yi)=πysinh ⁣(πy)\left|\Gamma\!\left(y i\right)\right| = \sqrt{\frac{\pi}{y \sinh\!\left(\pi y\right)}}
Assumptions:yR{0}y \in \mathbb{R} \setminus \left\{0\right\}
\left|\Gamma\!\left(y i\right)\right| = \sqrt{\frac{\pi}{y \sinh\!\left(\pi y\right)}}

y \in \mathbb{R} \setminus \left\{0\right\}
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:
    Formula(Equal(Abs(GammaFunction(Mul(y, ConstI))), Sqrt(Div(ConstPi, Mul(y, Sinh(Mul(ConstPi, y))))))),
    Assumptions(Element(y, SetMinus(RR, Set(0)))))

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

2019-09-16 21:17:18.797188 UTC