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Fungrim entry: 3b806f

η ⁣(1τ)=(iτ)1/2η ⁣(τ)\eta\!\left(-\frac{1}{\tau}\right) = {\left(-i \tau\right)}^{1 / 2} \eta\!\left(\tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta\!\left(-\frac{1}{\tau}\right) = {\left(-i \tau\right)}^{1 / 2} \eta\!\left(\tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
Powab{a}^{b} Power
ConstIii Imaginary unit
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("3b806f"),
    Formula(Equal(DedekindEta(Neg(Div(1, tau))), Mul(Pow(Neg(Mul(ConstI, tau)), Div(1, 2)), DedekindEta(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.

2019-08-19 14:38:23.809000 UTC