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|Title:||On generalized Vietoris’ number sequences|
Falcão, M. I.
Malonek, Helmuth R.
Hypercomplex Appell polynomials
Vietoris’ number sequence
|Journal:||Discrete 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.|
|Appears in Collections:||CMAT - Artigos em revistas com arbitragem / Papers in peer review journals|
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