GENERALIZATION OF FIBONACCI POLYNOMIALS

Fibonacci polynomials are special cases of Chebyshev polynomials and have been studied on a more advanced level by many mathematicians. Fibonacci polynomials are defined by fn+1=xfn(x)+fn-1(x), n>=1 with f0(x)=0, f1(x)=1. The Fibonacci polynomials are of great importance in the study of many subjects, such as algebra, geometry, and number theory itself. Obviously, they have a deep relationship with the famous Fibonacci sequence. That is fn(1)=Fn, where Fn is a Fibonacci number. In this paper, we introduce the generalization of Fibonacci polynomials by changing the initial terms with preservation of recurrence relation. Furthermore, some properties and identities of generalized Fibonacci polynomials are established and derived by standard methods.