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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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An elliptic $BC_n$ Bailey Lemma, multiple Rogers–Ramanujan identities and Euler’s Pentagonal Number Theorems
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by Hasan Coskun PDF
Trans. Amer. Math. Soc. 360 (2008), 5397-5433 Request permission

Abstract:

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 $_6\varphi _5$ 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 $B_n$ and $D_n$ generalizations of the Rogers–Ramanujan identities in terms of determinants of theta functions. Starting with the $BC_n$ $_6\varphi _5$ summation formula, a similar program is followed to prove an infinite family of $D_n$ Euler Pentagonal Number Theorems.
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Additional Information
  • Hasan Coskun
  • Affiliation: Department of Mathematics, Binnion Hall, Room 314, Texas A&M University–Com- merce, Commerce, Texas 75429
  • Email: hasan\_coskun@tamu-commerce.edu
  • Received by editor(s): May 22, 2006
  • Received by editor(s) in revised form: August 9, 2006, and October 16, 2006
  • Published electronically: April 17, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5397-5433
  • MSC (2000): Primary 05A19, 11B65; Secondary 05E20, 33D67
  • DOI: https://doi.org/10.1090/S0002-9947-08-04457-7
  • MathSciNet review: 2415079