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Glasgow Mathematical Journal (1)

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COMMON SOURCE OF NUMEROUS THETA FUNCTION IDENTITIES
CHU WENCHANG
Journal:

Glasgow Mathematical Journal / Volume 49 / Issue 1 / January 2007

Published online by Cambridge University Press:

01 January 2007, pp. 61-79

Print publication:

January 2007
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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 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.