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Title: Intrinsic properties of a non-symmetric number triangle
Author: Cação, Isabel
Malonek, Helmuth R.
Falcão, M. Irene
Tomaz, Graça
Keywords: Fibonacci sequence
Hypergeometric function
Hypercomplex analysis
Recurrence relation
Issue Date: 2023
Publisher: University of Waterloo
Abstract: Several authors are currently working on generalized Appell polynomials and their applications in the framework of hypercomplex function theory in Rn+1. A few years ago, two of the authors of this paper introduced a prototype of these generalized Appell polynomials, which heavily draws on a one-parameter family of non-symmetric number triangles T (n), n ≥ 2. In this paper, we prove several new and interesting properties of finite and infinite sums constructed from entries of T (n), similar to the ordinary Pascal triangle, which is not a part of that family. In particular, we obtain a recurrence relation for a family of finite sums, analogous to the ordinary Fibonacci sequence, and derive its corresponding generating function.
Peer review: yes
ISSN: 1530-7638
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Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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