A generalized quaternionic sequence with Vietoris' number components

SAÇLI G. Y.

Filomat, cilt.37, sa.28, ss.9753-9768, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 28
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2298/fil2328753s
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9753-9768
  • Anahtar Kelimeler: Binet’s formula, Catalan’s identity, generalized quaternion, generating function, recurrence relation, Vietoris' number sequence
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.