# Fungrim entry: a0ba58

$\frac{\theta_{3}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)} = \prod_{n=1}^{\infty} {\left(\frac{1 + {q}^{2 n - 1}}{1 - {q}^{2 n - 1}}\right)}^{2}\; \text{ where } q = {e}^{\pi i \tau}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\frac{\theta_{3}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)} = \prod_{n=1}^{\infty} {\left(\frac{1 + {q}^{2 n - 1}}{1 - {q}^{2 n - 1}}\right)}^{2}\; \text{ where } q = {e}^{\pi i \tau}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
Product$\prod_{n} f(n)$ Product
Pow${a}^{b}$ Power
Infinity$\infty$ Positive infinity
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("a0ba58"),
Formula(Equal(Div(JacobiTheta(3, 0, tau), JacobiTheta(4, 0, tau)), Where(Product(Pow(Div(Add(1, Pow(q, Sub(Mul(2, n), 1))), Sub(1, Pow(q, Sub(Mul(2, n), 1)))), 2), For(n, 1, Infinity)), Equal(q, Exp(Mul(Mul(Pi, ConstI), tau)))))),
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.

2020-01-31 18:09:28.494564 UTC