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Integral and series representations of $ q$-polynomials and functions: Part II Schur polynomials and the Rogers-Ramanujan identities

Authors: Mourad E. H. Ismail and Ruiming Zhang
Journal: Proc. Amer. Math. Soc. 145 (2017), 3717-3733
MSC (2010): Primary 11P84, 33D45; Secondary 05A17
Published electronically: May 24, 2017
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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

Ruiming Zhang
Affiliation: College of Science, Northwest A&F University, Yangling, Shaanxi 712100, People’s Republic of China

Keywords: Rogers-Ramanujan identities, $m$-versions, the Ramanujan function, Stieltjes--Wigert polynomials, bilateral $q$-series
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
Article copyright: © Copyright 2017 American Mathematical Society

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