Tribasic integrals and identities of Rogers-Ramanujan type
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- by M. E. H. Ismail and D. Stanton PDF
- Trans. Amer. Math. Soc. 355 (2003), 4061-4091 Request permission
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.References
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Additional Information
- M. E. H. Ismail
- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- MR Author ID: 91855
- D. Stanton
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4061-4091
- MSC (2000): Primary 33D45, 10J20; Secondary 33E20
- DOI: https://doi.org/10.1090/S0002-9947-03-03338-5
- MathSciNet review: 1990575