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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tribasic integrals and identities of Rogers-Ramanujan type


Authors: M. E. H. Ismail and D. Stanton
Journal: Trans. Amer. Math. Soc. 355 (2003), 4061-4091
MSC (2000): Primary 33D45, 10J20; Secondary 33E20
Published electronically: June 24, 2003
MathSciNet review: 1990575
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Abstract: Some integrals involving three bases are evaluated as infinite products using complex analysis. Many special cases of these integrals may be evaluated in another way to find infinite sum representations for these infinite products. The resulting identities are identities of Rogers-Ramanujan type. Some integer partition interpretations of these identities are given. Generalizations of the Rogers-Ramanujan type identities involving polynomials are given again as corollaries of integral evaluations.


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Additional Information

M. E. H. Ismail
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816

D. Stanton
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03338-5
PII: S 0002-9947(03)03338-5
Received by editor(s): June 16, 2002
Published electronically: June 24, 2003
Additional Notes: This research was partially supported by NSF grants DMS 99-70865, DMS 99-70627, and the Liu Bie Ju Center for Mathematical Sciences
Article copyright: © Copyright 2003 American Mathematical Society