Umbral calculus, Bailey chains, and pentagonal number theorems

George E. Andrews

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We revisit the umbral methods used by L. J. Rogers in his second proof of the Rogers-Ramanujan identities. We shall study how subsequent methods such as the Bailey chains and their variants arise naturally from Rogers' insights. We conclude with the introduction of multi-dimensional Bailey chains and apply them to prove some new Pentagonal Number Theorems.

Original languageEnglish (US)
Pages (from-to)464-475
Number of pages12
JournalJournal of Combinatorial Theory. Series A
Issue number1-2
StatePublished - Jul 2000

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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