Some identities of bivariate Pell and bivariate Pell-Lucas polynomials

Abstract

In this paper, we obtain some identities for the bivariate Pell polynomials and bivariate Pell-Lucas polynomials. We establish some sums and connection formulas involving them. Moreover, we present its two cross two matrices representation and find some of its properties, such as the b^th power of the matrix. We finally derive the identities by using Binet’s formula, generating function, and induction method.

Keywords

• Bivariate Pell polynomials
• bivariate Pell-Lucas polynomials
• Binet’s formula
• generating function

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