Carlitz and the general 3φ2

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Abstract

In a letter dated March 3, 1971, L. Carlitz defined a sequence of polynomials, Φn (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 Φn (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).

Original languageEnglish (US)
Pages (from-to)311-318
Number of pages8
JournalRamanujan Journal
Volume13
Issue number1-3
DOIs
StatePublished - Jun 2007

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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