An Elliptic $BC_n$ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems
| dc.creator | Coskun, Hasan | |
| dc.date | 2006-05-24 | |
| dc.date | 2006-11-22 | |
| dc.date.accessioned | 2026-07-07T07:14:30Z | |
| dc.date.available | 2026-07-07T07:14:30Z | |
| dc.description | An elliptic $BC_n$ generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter $BC_n$ Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system $BC_n$ are proved as applications, including a $_6ϕ_5$ summation formula, a generalized Watson transformation and an unspecialized Rogers--Selberg identity. The last identity is specialized to give an infinite family of multilateral Rogers--Selberg identities. Standard determinant evaluations are then used to compute $B_n$ and $D_n$ generalizations of the Rogers--Ramanujan identities in terms of determinants of theta functions. Starting with the $BC_n$ $_6ϕ_5$ summation formula, a similar program is followed to prove an infinite family of $D_n$ Euler's Pentagonal Number Theorems. | |
| dc.description | V2: 36 pages; to appear in AMS Trans; references added; typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0605653 | |
| dc.identifier | http://arxiv.org/abs/math/0605653 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112902 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05A19; 11B65; 05E20; 33D67 | |
| dc.title | An Elliptic $BC_n$ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems | |
| dc.type | text |