Geodesic
A generalized quaternionic sequence with Vietoris' number components
Filomat, Tome 37 (2023) no. 28, p. 9753

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DOI

In this investigation, the aim is to determine a generalized quaternionic sequence with Vietoris' number components depending on 2-parameters α and β. Considering specific real values α and β, various types of classical quaternionic sequence with Vietoris' number components can be obtained as real, split, split-semi and so on. The fundamental algebraic structures, several classical expressions, a two and three term recurrence relations are identified, as well as Catalan-like, generating function and Binet-like formulas. Furthermore, a determinantal approach is used to generate the generalized quaternionic sequence with Vietoris' number components.
DOI : 10.2298/FIL2328753S
Classification : 11R52, 11B37, 05A10, 11K31
Keywords: Vietoris' number sequence, generalized quaternion, recurrence relation, Catalan’s identity, generating function, Binet’s formula 
Gülsüm Yeliz Şentürk. A generalized quaternionic sequence with Vietoris' number components. Filomat, Tome 37 (2023) no. 28, p. 9753 . doi: 10.2298/FIL2328753S
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     title = {A generalized quaternionic sequence with {Vietoris'} number components},
     journal = {Filomat},
     pages = {9753 },
     year = {2023},
     volume = {37},
     number = {28},
     doi = {10.2298/FIL2328753S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2328753S/}
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