d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations

Year 2022, Volume: 14 Issue: 2, 262 - 270, 30.12.2022

Engin Özkan , Mine Uysal

https://doi.org/10.47000/tjmcs.1007382

Abstract

We define a new generalization of Gaussian Pell-Lucas polynomials. We call it $d-$Gaussian Pell-Lucas polynomials. Then we present the generating function and Binet formula for the polynomials. We give a matrix representation of $d-$Gaussian Pell-Lucas polynomials. Using the Riordan method, we obtain the factorizations of Pascal matrix involving the polynomials.

Keywords

d-Gaussian Pell-Lucas polynomial, generating function, Binet formula, Riordan matrix, d-Gaussian Pell-Lucas polynomial matrix

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