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).
KeywordsAl-salam-Carlitz polynomials q-hypergeometric series
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- 3.Andrews, G.E.: The Theory of Partitions. Encyl. of Math. and Its Appl., vol. 2, Addison-Wesley, Reading, (1976) (reissued: Cambridge University Press, Cambridge (1985, 1998))Google Scholar
- 4.Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyl. of Math. and Its Appl., vol. 35, Cambridge University Press, Cambridge (1990)Google Scholar