Jacobi's Triple-Product Identity and an Associated Family of Theta-Function Identities.

The main object of this paper is to present a family of -series identities which involve some of the theta functions of Jacobi and Ramanujan. Each of these (presumably new) -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 results presented in this paper are motivated essentially by a number of recent works dealing with the subject matter which is investigated herein. [ABSTRACT FROM AUTHOR]