$d-$Fibonacci and $d-$Lucas polynomials

Document Type : Research Paper

Authors

1 LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 Algeria

2 LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, Algeria

Abstract

Riordan arrays give us an intuitive method of solving combinatorial problems. They also help to apprehend number patterns and to prove many theorems. In this paper, we consider the Pascal matrix, define a new generalization of Fibonacci and Lucas polynomials called $d-$Fibonacci and $d-$Lucas polynomials (respectively) and  provide their properties. Combinatorial identities are obtained for the defined polynomials and by using Riordan method we get factorizations of Pascal matrix involving $d-$Fibonacci polynomials.

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