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The Ramanujan Journal

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

Carlitz and the general 3φ2

Article

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).

Keywords

Al-salam-Carlitz polynomials q-hypergeometric series 

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References

  1. 1.
    Al-Salam, W., Carlitz, L.: Some q-orthogonal polynomials. Math. Nach. 30, 47–61 (1965)MathSciNetGoogle Scholar
  2. 2.
    Andrews, G.E.: Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, 618–622 (1972)MathSciNetGoogle Scholar
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    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
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    Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyl. of Math. and Its Appl., vol. 35, Cambridge University Press, Cambridge (1990)Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityUniversity Park

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