Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/47203

TitleOn Vietoris' number sequence and combinatorial identities with quaternions
Author(s)Cação, I.
Falcão, M. I.
Malonek, H. R.
KeywordsVietoris' number sequence
Quaternions
Combinatorial identities
Issue date2017
Abstract(s)Ruscheweyh and Salinas showed in 2004 the relationship of a celebrated theorem of Vietoris (1958) about the positivity of certain sine and cosine sums with the function theoretic concept of stable holomorphic functions in the unit disc. The present paper reveals that the coefficient sequence in Vietoris' theorem is identical to a number sequence obtained by a new combinatorial identity which involves generators of quaternions. In this sense Vietoris' sequence of rational numbers combines seemingly disperse subjects in Real, Complex and Hypercomplex Analysis. Thereby we show that a non-standard application of Clifford algebra tools is able to reveal new insights in objects of combinatorial nature.
TypeConference paper
URIhttp://hdl.handle.net/1822/47203
ISBN978-84-617-8694-7
Publisher versionhttp://cmmse.usal.es/cmmse2017/sites/default/files/volumes/Proceedings_CMMSE_2017_vol_1_6.pdf
Peer-Reviewedyes
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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