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Fungrim entry: b7a578

cos ⁣(πz)=πΓ ⁣(12+z)Γ ⁣(12z)\cos\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(\frac{1}{2} + z\right) \Gamma\!\left(\frac{1}{2} - z\right)}
Assumptions:zCz \in \mathbb{C}
TeX:
\cos\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(\frac{1}{2} + z\right) \Gamma\!\left(\frac{1}{2} - z\right)}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Coscos(z)\cos(z) Cosine
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("b7a578"),
    Formula(Equal(Cos(Mul(Pi, z)), Div(Pi, Mul(Gamma(Add(Div(1, 2), z)), Gamma(Sub(Div(1, 2), z)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC