A Generalization of Schröter’s Formula

Abstract

We prove a generalization of Schröter’s formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the well-known identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist’s Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q) ∞ and (q;q)∞k, k≥ 3 , as combinations of Jacobi triple products, are also proved.