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Fungrim entry: d38a03

sin ⁣(πz)=πΓ ⁣(z)Γ ⁣(1z)\sin\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(z\right) \Gamma\!\left(1 - z\right)}
Assumptions:zCz \in \mathbb{C}
TeX:
\sin\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(z\right) \Gamma\!\left(1 - z\right)}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ConstPiπ\pi The constant pi (3.14...)
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("d38a03"),
    Formula(Equal(Sin(Mul(ConstPi, z)), Div(ConstPi, Mul(GammaFunction(z), GammaFunction(Sub(1, z)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2019-08-21 11:44:15.926409 UTC