Fungrim entry: a9c825

\theta_{2}\!\left(0 , \tau\right) = \frac{2 \eta^{2}\!\left(2 \tau\right)}{\eta(\tau)}

Assumptions:

\tau \in \mathbb{H}

TeX:

\theta_{2}\!\left(0 , \tau\right) = \frac{2 \eta^{2}\!\left(2 \tau\right)}{\eta(\tau)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`Pow`	${a}^{b}$	Power
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("a9c825"),
    Formula(Equal(JacobiTheta(2, 0, tau), Div(Mul(2, Pow(DedekindEta(Mul(2, tau)), 2)), DedekindEta(tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Jacobi theta functions

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