Fungrim entry: 85b2ff

\theta_{3}\!\left(0 , \tau\right) = \frac{\eta^{2}\!\left(\frac{1}{2} \left(\tau + 1\right)\right)}{\eta\!\left(\tau + 1\right)}

Assumptions:

\tau \in \mathbb{H}

TeX:

\theta_{3}\!\left(0 , \tau\right) = \frac{\eta^{2}\!\left(\frac{1}{2} \left(\tau + 1\right)\right)}{\eta\!\left(\tau + 1\right)}

\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("85b2ff"),
    Formula(Equal(JacobiTheta(3, 0, tau), Div(Pow(DedekindEta(Mul(Div(1, 2), Add(tau, 1))), 2), DedekindEta(Add(tau, 1))))),
    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