Change of base in Bailey pairs

1999/09/09 by David M. Bressoud, David Bressoud, Mourad E. H. Ismail +5 · 5 citations
Mathematics · #05A17 #11P81 #17B68 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A17 #msc:11P81 #msc:17B68

paper · pdf · doi:10.48550/arxiv.math/9909053

arxiv created 1999/09/09 · openalex publication_date 1999/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Versions of Bailey's lemma which change the base from q to q² or q³ are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities. We also prove Melzer's conjectures for the Fermionic forms of the supersymmetric analogues of Virasoro characters.

Cited by

• Modularity of Nahm Sums Dual to Zagier's Rank-Three Examples
• Nahm sum identities for Cartan matrices of type D_k
• Affine Jacobi-Trudi formulas and q,t-Rogers-Ramanujan identities
• Bailey pairs and quantum q-series identites. I. The classical identities
• Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples

Related

• Two new Bailey pairs and their q-identities of Rogers-Ramanujan type modulo 15, 24, and 30
• Shifted versions of the Bailey and well-poised Bailey lemmas
• An A₂ Bailey lemma and Rogers--Ramanujan-type identities
• Bilateral Bailey pairs and Rogers-Ramanujan type identities
• Bailey Type Transforms and Applications