nLab
Jacobi triple product

Statetement

The equation

n=1(1x 2n)(1x 2n1y 2)(1x 2n1y 2)=n=x 2ny 2n \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).

References

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

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

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