A NEW FAMILIES OF GAUSS k-JACOBSTHAL NUMBERS AND GAUSS k-JACOBSTHAL-LUCAS NUMBERS AND THEIR POLYNOMIALS

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Özkan E., Taştan M.

JOURNAL OF SCIENCE AND ARTS, sa.4, ss.893-908, 2020 (Hakemli Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.46939/j.sci.arts-20.4-a10
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Other Indexes
  • Sayfa Sayıları: ss.893-908
  • Marmara Üniversitesi Adresli: Hayır

Özet

In this paper, we define the new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers. We obtain some exciting properties of the families. We give the relationships between the family of the Gauss k-Jacobsthal numbers and the known Gauss Jacobsthal numbers, the family of the Gauss k-Jacobsthal-Lucas numbers and the known Gauss Jacobsthal-Lucas numbers. We also define the generalized polynomials for these numbers. Further, we obtain some interesting properties of the polynomials. In addition, we give the relationships between the generalized Gauss k-Jacobsthal polynomials and the known Gauss Jacobsthal polynomials, the generalized Gauss k-Jacobsthal-Lucas polynomials and the known Gauss Jacobsthal-Lucas polynomials. Furthermore, we find the new generalizations of these families and the polynomials in matrix representation. Then we prove Cassini's Identities for the families and their polynomials.