Bailey Type Transforms and Applications

Abstract

The aim of this paper is to establish new series transforms of Bailey type and to show that these Bailey type transforms work as efficiently as the classical one and give not only new $q$-hypergeometric identities, converting double or triple series into a very-well-poised ${}_{10}{\Phi }_9$ or ${}_{12}{\Phi }_{11}$ series but can also be utilized to derive new double and triple series Rogers-Ramanujan type identities and corresponding infinite families of Rogers-Ramanujan type identities.

31 pages

References in corpus (8)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
• Virasoro character identities from the Andrews--Bailey construction
• Identities of the Rogers--Ramanujan--Slater Type
• A Higher-level Bailey Lemma
• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma
• $q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type
• Identities of the Rogers--Ramanujan--Bailey Type

Cited by in corpus (3)

• Some implications of the $2$-fold Bailey lemma
• An interesting $q$-series related to the 4-th symmetrized rank function
• A partition identity connected to the second rank moment