Jacobi Triple Product

The Jacobi triple product is a mathematical identity discovered by Carl Gustav Jacob Jacobi and published in 1829 in his book on the theory of elliptic functions, Fundamenta Nova Theoriae Functionum Ellipticarum. It states that an infinite product built from terms of the form (1 minus x to the 2m), (1 plus x to the 2m-1 times y squared), and (1 plus x to the 2m-1 divided by y squared) equals an infinite sum of terms of the form x to the n squared times y to the 2n, for complex numbers x and y with the absolute value of x less than 1 and y not equal to zero. The identity has deep connections elsewhere in mathematics: it is the Macdonald identity for the affine root system of type A1, and it is the Weyl denominator formula for the corresponding affine Kac-Moody algebra. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/