d-Gaussian Pell-Lucas Polynomials and Their Matrix Representations

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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