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Fungrim entry: 53026a

Γ(z)=2πexp ⁣(ζ ⁣(0,z))\Gamma(z) = \sqrt{2 \pi} \exp\!\left(\zeta'\!\left(0, z\right)\right)
Assumptions:zC{0,1,}z \in \mathbb{C} \setminus \{0, -1, \ldots\}
\Gamma(z) = \sqrt{2 \pi} \exp\!\left(\zeta'\!\left(0, z\right)\right)

z \in \mathbb{C} \setminus \{0, -1, \ldots\}
Fungrim symbol Notation Short description
GammaΓ(z)\Gamma(z) Gamma function
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Expez{e}^{z} Exponential function
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(Gamma(z), Mul(Sqrt(Mul(2, Pi)), Exp(HurwitzZeta(0, z, 1))))),
    Assumptions(Element(z, SetMinus(CC, ZZLessEqual(0)))))

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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