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Fungrim entry: ff587a

η ⁣(τ)=eπiτ/12ϕ ⁣(e2πiτ)\eta\!\left(\tau\right) = {e}^{\pi i \tau / 12} \phi\!\left({e}^{2 \pi i \tau}\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta\!\left(\tau\right) = {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\!\left(\tau\right) Dedekind eta function
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
EulerQSeriesϕ ⁣(q)\phi\!\left(q\right) 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(ConstPi, ConstI), tau), 12)), EulerQSeries(Exp(Mul(Mul(Mul(2, ConstPi), ConstI), 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.

2019-08-19 14:38:23.809000 UTC