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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:yR{0}y \in \mathbb{R} \setminus \left\{0\right\}
\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\}
Fungrim symbol Notation Short description
Absz\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:
    Formula(Equal(Abs(Gamma(Add(1, Mul(y, ConstI)))), Sqrt(Div(Mul(Pi, y), Sinh(Mul(Pi, y)))))),
    Assumptions(Element(y, SetMinus(RR, Set(0)))))

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2021-03-15 19:12:00.328586 UTC