Opuscula Math. 32, no. 4 (2012), 661-673
A note on a one-parameter family of non-symmetric number triangles
Maria Irene Falcão
Helmuth R. Malonek
Abstract. The recent growing interest in special Clifford algebra valued polynomial solutions of generalized Cauchy-Riemann systems in \((n + 1)\)-dimensional Euclidean spaces suggested a detailed study of the arithmetical properties of their coefficients, due to their combinatoric relevance. This concerns, in particular, a generalized Appell sequence of homogeneous polynomials whose coefficient set can be treated as a one-parameter family of non-symmetric triangles of fractions. The discussion of its properties, similar to those of the ordinary Pascal triangle (which itself does not belong to the family), is carried out in this paper.
Keywords: Clifford analysis, generalized Appell polynomials, number triangle, central binomial coefficient, binomial identity.
Mathematics Subject Classification: 30G35, 11B65, 05A19.