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Fungrim entry: ee56b9

tan⁡ ⁣(πz)=Γ ⁣(12+z)Γ ⁣(12−z)Γ(z)Γ ⁣(1−z)\tan\!\left(\pi z\right) = \frac{\Gamma\!\left(\frac{1}{2} + z\right) \Gamma\!\left(\frac{1}{2} - z\right)}{\Gamma(z) \Gamma\!\left(1 - z\right)}
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\tan\!\left(\pi z\right) = \frac{\Gamma\!\left(\frac{1}{2} + z\right) \Gamma\!\left(\frac{1}{2} - z\right)}{\Gamma(z) \Gamma\!\left(1 - z\right)}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Piπ\pi The constant pi (3.14...)
GammaΓ(z)\Gamma(z) Gamma function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("ee56b9"),
    Formula(Equal(Tan(Mul(Pi, z)), Div(Mul(Gamma(Add(Div(1, 2), z)), Gamma(Sub(Div(1, 2), z))), Mul(Gamma(z), Gamma(Sub(1, z)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC