A Family of Theta-Function Identities Related to Jacobi’s Triple-Product Identity

Abstract

The main object of this paper is to present a family of q-series identities which involve some of the theta functions of Jacobi and Ramanujan. Each of these (presumably new) q-series identities reveals interesting relationships among three of the theta-type functions which stem from the celebrated Jacobi’s triple-product identity in a remarkably simple way. The q-results presented in this paper are motivated essentially by recent works of Chaudhary et al. (see [4, 5]) and of other authors (see, for example, [1, 13]).