General quadratic decomposition
Ângela Macedo, P. Maroni · The Journal of Difference Equations and Applications · 2010
A general quadratic decomposition of polynomial sequences is carried out. This generalizes the works of L. Carlitz, Boll. Un. Mat. Ital. 16 (1961), pp. 386–390; L.M. Chihara and T.S. Chihara, J. Math. Anal. Appl. 126 (1987), pp. 275–291; T.S. Chihara, Boll. Un. Mat. Ital. 19 (1964), pp. 451–459 and that of P. Maroni, Rev. Math. Pura ed Appl. (6) (1990), pp. 19–53. We deal with the transformation , where instead of that where p and q are zero. We give the general quadratic decomposition of a monic polynomial sequence. The characterization of the cases where is orthogonal are given.