Fungrim entry: f04e01

\varepsilon\!\left(1, b, 0, 1\right) = {e}^{\pi i b / 12}

b \in \mathbb{Z}

TeX:

\varepsilon\!\left(1, b, 0, 1\right) = {e}^{\pi i b / 12}

Definitions:

Fungrim symbol	Notation	Short description
`DedekindEtaEpsilon`	$\varepsilon\!\left(a, b, c, d\right)$	Root of unity in the functional equation of the Dedekind eta function
`Exp`	${e}^{z}$	Exponential function
`ConstPi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("f04e01"),
    Formula(Equal(DedekindEtaEpsilon(1, b, 0, 1), Exp(Div(Mul(Mul(ConstPi, ConstI), b), 12)))),
    Variables(b),
    Element(b, ZZ))

Topics using this entry

Dedekind eta function

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

2019-06-18 07:49:59.356594 UTC