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Title: On generalized Vietoris’ number sequences
Author: Cação, Isabel
Falcão, M. Irene
Malonek, Helmuth R.
Keywords: Vietoris’ number sequence
Hypercomplex Appell polynomials
Generating function
Recurrence relation
Issue Date: 30-Sep-2019
Publisher: Elsevier
Abstract: Recently, by using methods of hypercomplex function theory, the authors have shown that a certain sequence S of rational numbers (Vietoris’ sequence) combines seemingly disperse subjects in real, complex and hypercomplex analysis. This sequence appeared for the first time in a theorem by Vietoris (1958) with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/Salinas, 2004). A non-standard application of Clifford algebra tools for defining Clifford-holomorphic sequences of Appell polynomials was the hypercomplex context in which a one-parametric generalization S(n), n ≥ 1, of S (corresponding to n = 2) surprisingly showed up. Without relying on hypercomplex methods this paper demonstrates how purely real methods also lead to S(n). For arbitrary n ≥ 1 the generating function is determined and for n = 2 a particular case of a recurrence relation similar to that known for Catalan numbers is proved.
Peer review: yes
DOI: 10.1016/j.dam.2018.10.017
ISSN: 0166-218X
Appears in Collections:CIDMA - Artigos
DMat - Artigos
CHAG - Artigos

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