Gaussian Pell and Gaussian Pell-Lucas Quaternions

ARSLAN H.

FILOMAT, cilt.35, sa.5, ss.1609-1617, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2298/fil2105609a
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.1609-1617
  • Anahtar Kelimeler: Gaussian Pell and Gaussian Pell-Lucas numbers, recurrence relations, quaternions, generating functions, FIBONACCI, NUMBERS
  • Erciyes Üniversitesi Adresli: Evet

Özet

The main aim of this work is to introduce the Gaussian Pell quaternion QGp(n) and Gaussian Pell-Lucas quaternion OGq(n), where the components of QGp(n) and QGq(n) are Pell numbers p(n) and Pell-Lucas numbers q(n), respectively. Firstly, we obtain the recurrence relations and Binet formulas for QGp(n) and QGq(n). We use Binet formulas to prove Cassini's identity for these quaternions. Furthermore, we give some basic identities for QGp(n) and OGq(n) such as some summation formulas, the terms with negative indices and the generating functions for these complex quaternions.