Combinatorial proofs of certain identities involving partial theta functions

Byungchan Kim

doi:10.1142/S1793042110003046

Combinatorial proofs of certain identities involving partial theta functions

Byungchan Kim

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In this brief note, we give combinatorial proofs of two identities involving partial theta functions. As an application, we prove an identity for the product of partial theta functions, first established by Andrews and Warnaar. We also provide a generalization of the first two identities and give a combinatorial proof of the generalized identities.

Original language	English
Pages (from-to)	449-460
Number of pages	12
Journal	International Journal of Number Theory
Volume	6
Issue number	2
DOIs	https://doi.org/10.1142/S1793042110003046
State	Published - Mar 2010

Keywords

Partial theta function
Partition
Ramanujan's lost notebook

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AB - In this brief note, we give combinatorial proofs of two identities involving partial theta functions. As an application, we prove an identity for the product of partial theta functions, first established by Andrews and Warnaar. We also provide a generalization of the first two identities and give a combinatorial proof of the generalized identities.

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KW - Partition

KW - Ramanujan's lost notebook

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Combinatorial proofs of certain identities involving partial theta functions

Abstract

Keywords

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