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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Integral and series representations of $q$-polynomials and functions: Part II Schur polynomials and the Rogers-Ramanujan identities
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by Mourad E. H. Ismail and Ruiming Zhang PDF
Proc. Amer. Math. Soc. 145 (2017), 3717-3733 Request permission

Abstract:

We give several expansion and identities involving the Ramanujan function $A_q$ and the Stieltjes–Wigert polynomials. Special values of our identities give $m$-versions of some of the items on the Slater list of Rogers-Ramanujan type identities. We also study some bilateral extensions of certain transformations in the theory of basic hypergeometric functions.
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Additional Information
  • Mourad E. H. Ismail
  • Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
  • MR Author ID: 91855
  • Email: mourad.eh.ismail@gmail.com
  • Ruiming Zhang
  • Affiliation: College of Science, Northwest A&F University, Yangling, Shaanxi 712100, People’s Republic of China
  • MR Author ID: 257230
  • Email: ruimingzhang@yahoo.com
  • Received by editor(s): May 9, 2016
  • Received by editor(s) in revised form: May 11, 2016, June 9, 2016, and October 11, 2016
  • Published electronically: May 24, 2017
  • Additional Notes: Research partially supported by the DSFP of King Saud University and by the National Plan for Science, Technology and innovation (MAARIFAH), King Abdelaziz City for Science and Technology, Kingdom of Saudi Arabia, Award number 14-MAT623-02
    The second author is the corresponding author. His research was partially supported by the National Science Foundation of China, grant No. 11371294
  • Communicated by: Kathrin Bringmann
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 3717-3733
  • MSC (2010): Primary 11P84, 33D45; Secondary 05A17
  • DOI: https://doi.org/10.1090/proc/13535
  • MathSciNet review: 3665027