On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials

Year 2023, Volume: 72 Issue: 2, 407 - 416, 23.06.2023

Hayrullah Özimamoğlu , Ahmet Kaya

https://doi.org/10.31801/cfsuasmas.1138441

https://izlik.org/JA53RC34TH

Abstract

In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.

Keywords

Gaussian Pell-Lucas numbers , Gaussian Pell-Lucas polynomials , Cassini’s identity

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