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

Authors : Hayrullah ÖZİMAMOĞLU, Ahmet KAYA

Pages : 407-416

Doi:10.31801/cfsuasmas.1138441

View : 39 | Download : 66

Publication Date : 2023-06-23

Article Type : Research Paper

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, Cassinis identity