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
$q$-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 results presented in this paper are motivated essentially
by a number of recent works dealing with the subject matter
which is investigated herein.