Generalized Fibonacci-Lucas Polynomials

Abstract

Various sequences of polynomials by the names of Fibonacci and Lucas polynomials occur in the literature over a century. The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, Generalized Fibonacci-Lucas Polynomials are introduced and defined by the recurrence relation       n n-1 n-2 , b xb b x , n 2 x x    with   0 b 2 x b  and   1 b x s  . Some basic identities of Generalized Fibonacci-Lucas Polynomials are obtained by method of generating function.