Generalized Fibonacci Polynomials and some Identities

Abstract

The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities.Generalization of Fibonacci polynomial has been done using various approaches.One usually found in the literature that the generalization is done by varying the initial conditions.In this paper, Generalized Fibonacci polynomials are defined by 12 ( ) ( ) ( ); 2 n n n w x xw x w x n     with 0 ( ) 2 w x b  and 1 () w x a b , where a and b are integers.Further, some basic identities are generated and derived by generating function.