Jacobi triple product

The equation

$\underoverset{n=1}{\infty}{\prod}
\left(
1- x^{2n}
\right)
\left(
1- x^{2n-1} y^2
\right)
\left(
1- x^{2n-1} y^{-2}
\right)
=
\underoverset{n = -\infty}{\infty}{\sum}
x^{2n} y^{2n}$

Equivalently this is a relation between the four Jacobi theta functions (see there and at *Jacobi form*).

Due to

- Carl Jacobi,
*Fundamenta nova theoriae functionum ellipticarum*(in Latin), Königsberg: Borntraeger, ISBN 978-1-108-05200-9, Reprinted by Cambridge University Press 2012

Review includes

- Wikipedia,
*Jacobi triple product*

A large collection of identities between the various Jacobi theta functions related is at

- WolframResearch,
*Jacobi Thetas*

Created on September 10, 2014 at 19:41:18. See the history of this page for a list of all contributions to it.