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Fungrim entry: ff587a

η(τ)=eπiτ/12ϕ ⁣(e2πiτ)\eta(\tau) = {e}^{\pi i \tau / 12} \phi\!\left({e}^{2 \pi i \tau}\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta(\tau) = {e}^{\pi i \tau / 12} \phi\!\left({e}^{2 \pi i \tau}\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
EulerQSeriesϕ(q)\phi(q) Euler's q-series
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("ff587a"),
    Formula(Equal(DedekindEta(tau), Mul(Exp(Div(Mul(Mul(Pi, ConstI), tau), 12)), EulerQSeries(Exp(Mul(Mul(Mul(2, Pi), ConstI), tau)))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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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