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TitleVietoris' number sequence and its generalizations through hypercomplex function theory
Author(s)Cação, Isabel
Falcão, M. I.
Malonek, Helmuth
KeywordsVietoris' number sequence
Monogenic Appell polynomials
Generating functions
Issue date2018
Abstract(s)The so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the first time in a celebrated theorem by Vietoris (1958) about the positivity of certain trigonometric sums with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/ Salinas, 2004). In the context of hypercomplex function theory those numbers appear as coefficients of special homogeneous polynomials in R^3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in R^n.
TypeConference paper
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em atas de conferências e capítulos de livros com arbitragem / Papers in proceedings of conferences and book chapters with peer review

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