Transactions of the American Mathematical Society

An elliptic

Bailey Lemma, multiple Rogers-Ramanujan identities and Euler's Pentagonal Number Theorems

Author(s): Hasan Coskun
Journal: Trans. Amer. Math. Soc. 360 (2008), 5397-5433.
MSC (2000): Primary 05A19, 11B65; Secondary 05E20, 33D67
Posted: April 17, 2008
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Abstract: An elliptic

generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter

Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system

are proved as applications, including a $_6\varphi_5$ 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

and

generalizations of the Rogers-Ramanujan identities in terms of determinants of theta functions. Starting with the

$_6\varphi_5$ summation formula, a similar program is followed to prove an infinite family of

Euler Pentagonal Number Theorems.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 05A19, 11B65, 05E20, 33D67

Hasan Coskun
Affiliation: Department of Mathematics, Binnion Hall, Room 314, Texas A&M University--Commerce, Commerce, Texas 75429
Email: hasan\_coskun@tamu-commerce.edu

DOI: 10.1090/S0002-9947-08-04457-7
PII: S 0002-9947(08)04457-7
Keywords: Elliptic Bailey Lemma, multiple Rogers--Ramanujan identities, multiple Euler's Pentagonal Number Theorems, affine root systems, determinant evaluations, theta functions, Macdonald identities
Received by editor(s): May 22, 2006
Received by editor(s) in revised form: August 9, 2006 and October 16, 2006
Posted: April 17, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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