On a New Generalization of Bivariate Fibonacci Polynomials and Their Matrix Representations

Abstract

In this study, we introduce the concept of d-bivariate Fibonacci polynomials, which generalize the classical bivariate Fibonacci polynomials. We obtain several fundamental properties for these new polynomials including the generating function, the Binet’s formula, combinatorial identities and summation formulas. Then, we define the infinite d-bivariate Fibonacci polynomials matrix, which is a Riordan matrix. By Riordan method, we give two new factorizations of the infinite Pascal matrix including the d-bivariate Fibonacci polynomials.

Keywords

• Bivariate Fibonacci polynomials
• d-bivariate Fibonacci polynomials
• Pascal matrix
• Riordan matrix

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