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Fungrim entry: 1dc520

η(τ)=eπiτ/12k=1(1e2πikτ)\eta(\tau) = {e}^{\pi i \tau / 12} \prod_{k=1}^{\infty} \left(1 - {e}^{2 \pi i k \tau}\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\eta(\tau) = {e}^{\pi i \tau / 12} \prod_{k=1}^{\infty} \left(1 - {e}^{2 \pi i k \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
Productnf(n)\prod_{n} f(n) Product
Infinity\infty Positive infinity
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("1dc520"),
    Formula(Equal(DedekindEta(tau), Mul(Exp(Div(Mul(Mul(Pi, ConstI), tau), 12)), Product(Parentheses(Sub(1, Exp(Mul(Mul(Mul(Mul(2, Pi), ConstI), k), tau)))), For(k, 1, Infinity))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-12-11 23:01:54.699850 UTC