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COMMON SOURCE OF NUMEROUS THETA FUNCTION IDENTITIES

Published online by Cambridge University Press:  01 January 2007

CHU WENCHANG
CHU WENCHANG*
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
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Abstract.

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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.

Keywords

Primary 05A30Secondary 14K25

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 61 - 79
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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