A generalized quaternionic sequence with Vietoris' number components


SAÇLI G. Y.

Filomat, vol.37, no.28, pp.9753-9768, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 28
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2328753s
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.9753-9768
  • Keywords: Binet’s formula, Catalan’s identity, generalized quaternion, generating function, recurrence relation, Vietoris' number sequence
  • Istanbul Gelisim University Affiliated: Yes

Abstract

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.