A Bailey type identity with applications related to integer representations

Abstract

In this paper we shall deduce a Bailey type formula as a consequence of the residual identity of a q q -series transformation due to Gasper. Our formula leads to a variety of q q -series identities which are related to the arithmetic function counting integer representations of the form \[ n ( A n + B ) 2 + r ( C r + D ) 2 + E n r . \frac {n(An+B)}{2}+\frac {r(Cr+D)}{2} + Enr. \]