Carlitz and the general 3φ2 |
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Authors: | George E Andrews |
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Institution: | (1) The Pennsylvania State University, University Park, Pennsylvania, 16802 |
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Abstract: | In a letter dated March 3, 1971, L. Carlitz defined a sequence of polynomials, Φ
n
(a,b; x, y; z), generalizing the Al-Salam & Carlitz polynomials, but closely related thereto. He concluded the letter by stating: “It would
be of interest to find properties of Φ
n
(a, b; x, y; z) when all the parameters are free.” In this paper, we reproduce the Carlitz letter and show how a study of Carlitz’s polynomials
leads to a clearer understanding of the general 3Φ2 (a, b, c; d; e; q, z).
Dedicated to my friend, Richard Askey.
2000 Mathematics Subject Classification Primary—33D20.
G. E. Andrews: Partially supported by National Science Foundation Grant DMS 0200047. |
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Keywords: | Al-salam-Carlitz polynomials q-hypergeometric series |
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