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TitleHypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence
Author(s)Cação, Isabel
Falcão, M. I.
Malonek, Helmuth
KeywordsVietoris’ number sequence
Monogenic Appell polynomials
Generating functions
Issue date2017
PublisherSpringer Verlag
JournalComplex Analysis and Operator Theory
Abstract(s)This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients.
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AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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