Fungrim entry: 737805

\eta(\tau) = {e}^{\pi i \tau / 12} \theta_{3}\!\left(\frac{\tau + 1}{2} , 3 \tau\right)

Assumptions:

\tau \in \mathbb{H}

TeX:

\eta(\tau) = {e}^{\pi i \tau / 12} \theta_{3}\!\left(\frac{\tau + 1}{2} , 3 \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
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("737805"),
    Formula(Equal(DedekindEta(tau), Mul(Exp(Div(Mul(Mul(Pi, ConstI), tau), 12)), JacobiTheta(3, Div(Add(tau, 1), 2), Mul(3, tau))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Jacobi theta functions
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