On a new class of the generalized Gauss k-Pell numbers and their polynomials

Ahmet Kaya and Hayrullah Özimamoğlu
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 4, Pages 593–602
DOI: 10.7546/nntdm.2022.28.4.593-602
Full paper (PDF, 174 Kb)

Details

Authors and affiliations

Ahmet Kaya
Departments of Mathematics, Faculty of Arts and Sciences,
Nevşehir Hacı Bektaş Veli University
Nevşehir, 50300, Turkey

Hayrullah Özimamoğlu
Departments of Mathematics, Faculty of Arts and Sciences,
Nevşehir Hacı Bektaş Veli University
Nevşehir, 50300, Turkey

Abstract

In this article, we generalize the well-known Gauss Pell numbers and refer to them as generalized Gauss k-Pell numbers. There are relationships discovered between the class of generalized Gauss k-Pell numbers and the typical Gauss Pell numbers. Also, we generalize the known Gauss Pell polynomials, and call such polynomials as the generalized Gauss k-Pell polynomials. We obtain relations between the class of the generalized Gauss k-Pell polynomials and the typical Gauss Pell polynomials. Furthermore, we provide matrices for the novel generalizations of these numbers and polynomials. After that, we obtain Cassini’s identities for these numbers and polynomials.

Keywords

• Gauss Pell numbers
• Gauss Pell polynomials
• Gauss Fibonacci numbers
• Gauss Fibonacci polynomials
• Cassini’s identity

2020 Mathematics Subject Classification

• 11B37
• 11B39
• 11B83

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Manuscript history

• Received: 22 February 2022
• Revised: 21 September 2022
• Accepted: 30 September 2022
• Online First: 12 October 2022