Opuscula Math. 32, no. 4 (2012), 661-673
http://dx.doi.org/10.7494/OpMath.2012.32.4.661

 
Opuscula Mathematica

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.

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  • Maria Irene Falcão
  • University of Aveiro, Center for Research and Development in Mathematics and Applications
  • University of Minho, Department of Mathematics and Applications, Campus de Gualtar, 4710-057 Braga, Portugal
  • Helmuth R. Malonek
  • University of Aveiro, Department of Mathematics Center for Research and Development in Mathematics and Applications, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • Received: 2011-10-20.
  • Accepted: 2012-01-21.
Opuscula Mathematica - cover

Cite this article as:
Maria Irene Falcão, Helmuth R. Malonek, A note on a one-parameter family of non-symmetric number triangles, Opuscula Math. 32, no. 4 (2012), 661-673, http://dx.doi.org/10.7494/OpMath.2012.32.4.661

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