The Ramanujan Journal

, Volume 13, Issue 1–3, pp 311–318 | Cite as

Carlitz and the general 3φ2

  • George E. Andrews


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).


Al-salam-Carlitz polynomials q-hypergeometric series 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityUniversity Park

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