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).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory