TY - JOUR
T1 - Carlitz and the general 3φ2
AU - Andrews, George E.
N1 - Funding Information:
G. E. Andrews: Partially supported by National Science Foundation Grant DMS 0200047.
PY - 2007/6
Y1 - 2007/6
N2 - 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).
AB - 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).
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U2 - 10.1007/s11139-006-0254-0
DO - 10.1007/s11139-006-0254-0
M3 - Article
AN - SCOPUS:33845780490
SN - 1382-4090
VL - 13
SP - 311
EP - 318
JO - Ramanujan Journal
JF - Ramanujan Journal
IS - 1-3
ER -