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ISSN 1088-6850(e) ISSN 0002-9947(p)

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
MathSciNet review: 2415079
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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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