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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 qdifference 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.doi:10.1017/s0017089507003424 fatcat:r34dpgmp3ra7dhjmkmoghz4uwi