Bailey Pairs With Free Parameters, Mock Theta Functions and Tubular Partitions

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Abstract

This study began in an effort to find a simpler derivation of the Bailey pairs associated with the seventh order mock theta functions. It is shown that the introduction of a new parameter independent of both a and q leads to a much simpler treatment. It is noted that a previous treatment of the central fifth order mock theta function inadvertently uses this approach. The paper concludes by applying this method to find new surprising identities and new arithmetic objects, tubular partitions.

Original languageEnglish (US)
Pages (from-to)563-578
Number of pages16
JournalAnnals of Combinatorics
Volume18
Issue number4
DOIs
StatePublished - Nov 29 2014

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All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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