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Title: Vietoris' number sequence and its generalizations through hypercomplex function theory
Author: Cação, Isabel
Falcão, M. I.
Malonek, Helmuth
Keywords: Vietoris' number sequence
Monogenic Appell polynomials
Generating functions
Issue Date: 1-Nov-2018
Abstract: The so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the rst 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 coe cients of special homogeneous polynomials in R3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in Rn.
Peer review: yes
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