Generalized Bivariate Fibonacci-Like Polynomials and Some Identities
نویسندگان
چکیده
In [3], H. Belbachir and F. Bencherif generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. They prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations. [7], Mario Catalani define generalized bivariate polynomials, from which specifying initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. In [5], K. Inoue and S. Aki investigate the properties of bivariate Fibonacci polynomials of order k in terms of the generating functions. In [8], Mario Catalani derive a collection of identities for bivariate Fibonacci and Lucas polynomials using properties of such polynomials when the variables x and y are replaced by polynomials. A wealth of combinatorial identities can be obtained for selected values of the variables. In [8], Mario Catalani derived many interesting identities for Fibonacci and Lucas Polynomials, these identities derived from a book of Professor Gould. In [1], D. Tasci, M. C. Firengiz and N. Tuglu define the incomplete bivariate Fibonacci and Lucas p-polynomials also generating function and properties of the incomplete bivariate Fibonacci and Lucas p-polynomials are given. In this paper, we present generalized bivariate Fibonacci-Like polynomials sequence and its properties like Catalan’s identity, Cassini’s identity or Simpson’s identity and d’ocagnes’s identity for generalized bivariate Fibonacci-Like polynomials.
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