New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Alexander Berkovich, Ali Kemal Uncu

Research output: Contribution to journalArticlepeer-review


We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q↦1/q duality transformation of the base identities and some related partition theoretic relations.

Original languageEnglish
Article number125678
JournalJournal of Mathematical Analysis and Applications
Issue number2
Early online date21 Sep 2021
Publication statusE-pub ahead of print - 21 Sep 2021


  • Bailey's lemma
  • Capparelli's identities
  • Infinite hierarchies of q-series identities
  • q-binomial identities

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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