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Fungrim entry: 1bae52

η ⁣(τ+1)=eπi/12η(τ)\eta\!\left(\tau + 1\right) = {e}^{\pi i / 12} \eta(\tau)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta\!\left(\tau + 1\right) = {e}^{\pi i / 12} \eta(\tau)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("1bae52"),
    Formula(Equal(DedekindEta(Add(tau, 1)), Mul(Exp(Div(Mul(ConstPi, ConstI), 12)), DedekindEta(tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC