a1 Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
Motivated by the recent work due to Warnaar (2005), two new and elementary proofs are presented for a very useful q-difference equation on eight shifted factorials of infinite order. As the common source of theta function identities, this q-difference equation is systematically explored to review old and establish new identities on Ramanujan's partition functions. Most of the identities obtained can be interpreted in terms of theorems on classical partitions.
(Received January 27 2006)
(Accepted September 27 2006)
Work carried out during the visit to Dalian University of Technology (2005).