Fungrim entry: 1dc520

\eta(\tau) = {e}^{\pi i \tau / 12} \prod_{k=1}^{\infty} \left(1 - {e}^{2 \pi i k \tau}\right)

Assumptions:

\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
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`Product`	$\prod_{n} f(n)$	Product
`Infinity`	$\infty$	Positive infinity
`HH`	$\mathbb{H}$	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)))

Topics using this entry

Dedekind eta function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC