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# Fungrim entry: 7b3ac4

$\theta_{3}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau n\right)}$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
\theta_{3}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau n\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \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
Pi$\pi$ The constant pi (3.14...)
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("7b3ac4"),
Formula(Equal(Pow(JacobiTheta(3, 0, tau), 2), Sum(Div(1, Cos(Mul(Mul(Pi, tau), n))), For(n, Neg(Infinity), Infinity)))),
Variables(tau),
Assumptions(And(Element(z, CC), 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.

2020-01-31 18:09:28.494564 UTC