Intrinsic properties of a non-symmetric number triangle

• Autor(a) principal: Cação, Isabel
• Data de Publicação: 2023
• Outros Autores: Malonek, Helmuth R., Falcão, M. Irene, Tomaz, Graça
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/40086
• topic: Fibonacci sequence; Hypergeometric function; Hypercomplex analysis; Recurrence relation

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.