Аннотация:
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.
Ключевые слова:theta-function identities,
Jacobi's triple-product identity,
Ramanujan's theta functions,
$q$-series identities,
quadratic forms and elliptic functions,
number theory and the theory of partitions.
