# Fungrim entry: 9b7d8c

$\theta_{2}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau \left(n + \frac{1}{2}\right)\right)}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\theta_{2}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau \left(n + \frac{1}{2}\right)\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
Sum$\sum_{n} f(n)$ Sum
Cos$\cos(z)$ Cosine
Pi$\pi$ The constant pi (3.14...)
Infinity$\infty$ Positive infinity
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("9b7d8c"),
Formula(Equal(Pow(JacobiTheta(2, 0, tau), 2), Sum(Div(1, Cos(Mul(Mul(Pi, tau), Add(n, Div(1, 2))))), For(n, Neg(Infinity), Infinity)))),
Variables(tau),
Assumptions(Element(tau, HH)))

## Topics using this entry

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

2020-08-27 09:56:25.682319 UTC