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Generating functions for the generalized bivariate Fibonacci and Lucas polynomials. (English) Zbl 1318.11018

Summary: The main object of this study is to derive various families of multilinear and multilateral generating functions for the generalized bivariate Fibonacci and Lucas polynomials. Furthermore, we discuss some critical connections between the generalized bivariate Fibonacci, Lucas polynomials and the well-known polynomials and numbers, such as, bivariate and univariate Fibonacci and Lucas polynomials, the classical Fibonacci and Lucas numbers, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas and also the first and second kind Chebyshev polynomials.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
05A15 Exact enumeration problems, generating functions
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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