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Fungrim entry: a1a3d4

η ⁣(τ+12)=eπi/24η3 ⁣(2τ)η(τ)η ⁣(4τ)\eta\!\left(\tau + \frac{1}{2}\right) = {e}^{\pi i / 24} \frac{\eta^{3}\!\left(2 \tau\right)}{\eta(\tau) \eta\!\left(4 \tau\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta\!\left(\tau + \frac{1}{2}\right) = {e}^{\pi i / 24} \frac{\eta^{3}\!\left(2 \tau\right)}{\eta(\tau) \eta\!\left(4 \tau\right)}

\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
Powab{a}^{b} Power
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("a1a3d4"),
    Formula(Equal(DedekindEta(Add(tau, Div(1, 2))), Mul(Exp(Div(Mul(ConstPi, ConstI), 24)), Div(Pow(DedekindEta(Mul(2, tau)), 3), Mul(DedekindEta(tau), DedekindEta(Mul(4, tau))))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-10-05 13:11:19.856591 UTC