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Fungrim entry: f04e01

ε ⁣(1,b,0,1)=eπib/12\varepsilon\!\left(1, b, 0, 1\right) = {e}^{\pi i b / 12}
bZb \in \mathbb{Z}
TeX:
\varepsilon\!\left(1, b, 0, 1\right) = {e}^{\pi i b / 12}
Definitions:
Fungrim symbol Notation Short description
DedekindEtaEpsilonε ⁣(a,b,c,d)\varepsilon\!\left(a, b, c, d\right) Root of unity in the functional equation of the Dedekind eta function
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("f04e01"),
    Formula(Equal(DedekindEtaEpsilon(1, b, 0, 1), Exp(Div(Mul(Mul(Pi, ConstI), b), 12)))),
    Variables(b),
    Element(b, ZZ))

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

2019-11-19 15:10:20.037976 UTC