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Fungrim entry: b510b6

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

z \in \mathbb{C} \setminus \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
ConstPiπ\pi The constant pi (3.14...)
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("b510b6"),
    Formula(Equal(GammaFunction(z), Mul(Div(ConstPi, Sin(Mul(ConstPi, z))), Div(1, GammaFunction(Sub(1, z)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, ZZ))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC