WOOD v. BAILEY.

Lifting Bailey pairs to WP-Bailey pairs

A pair of sequences (αn(a, k, q),βn(a, k, q)) such that α0(a, k, q) = 1 and βn(a, k, q) = n ∑ j=0 (k/a; q)n−j(k; q)n+j (q; q)n−j(aq; q)n+j αj(a, k, q) is termed a WP-Bailey Pair. Upon setting k = 0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WPBailey pair, and use some of the new WP-Bailey pairs found in this way to derive...

Shifted versions of the Bailey and well-poised Bailey lemmas

The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive mversions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and obtain a new extension of the Rogers-Ramanujan identities.

Alphabetically ) : BAILEY - KELLOGG , CHRIS

Meeting Date: 10/13/2016 RFA/PA: PA16-302 Council: JAN 2017 PCC: M34 Requested Start: 07/01/2017 Dual PCC: P146SS Dual IC(s): GM Project Title: High-throughput, multiplexed characterization and modeling of antibody:antigen binding, with application to HSV SRG Action: Impact Score:18 Next Steps: Visit http://grants.nih.gov/grants/next_steps.htm Human Subjects: 10-No human subjects involved Anima...

A Bailey Lattice

We exhibit a technique for generating new Bailey pairs which leads to deformations of classical q-series identities, multiple series identities of the Rogers-Ramanujan type, identities involving partial theta functions, and a variety of representations for q-series by number theoretic objects like weight 3/2 modular forms, ternary quadratic forms, and weighted binary quadratic forms.

William Frederick Bailey Eadon