Please use this identifier to cite or link to this item:

TitleOn generalized Vietoris’ number sequences
Author(s)Cação, Isabel
Falcão, M. I.
Malonek, Helmuth R.
KeywordsGenerating function
Hypercomplex Appell polynomials
Recurrence relation
Vietoris’ number sequence
Issue date30-Sep-2019
PublisherElsevier B.V.
JournalDiscrete Applied Mathematics
Abstract(s)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.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

Files in This Item:
File Description SizeFormat 
CaFaMa_DAMRepositoriUM.pdf313,88 kBAdobe PDFView/Open

Partilhe no FacebookPartilhe no TwitterPartilhe no DeliciousPartilhe no LinkedInPartilhe no DiggAdicionar ao Google BookmarksPartilhe no MySpacePartilhe no Orkut
Exporte no formato BibTex mendeley Exporte no formato Endnote Adicione ao seu ORCID