Some Identities Of Fibonacci And Lucas Polynomials

Fibonacci numbers and Fibonacci polynomials always play an important role in number theory for solving problems involving the arithmetic function and polynomials. Identities involving Fibonacci polynomials, as special identities, has been studied together with the Lucas polynomials, Bernoulli polynomials Bi(t) and the Euler polynomials Ei(t), which has been kept close watch on and attached importance to by many scholars.In this dissertation, we study the properties of general Fibonacci polyno-mials Fn(x,y) and Lucas polynomials Ln{x,y) by the fundamental theory of analysis. By working with combinatorial summations, together with the gener-ating functions for Bernoulli polynomials and Euler polynomials, we obtain a series of identities.Thus we utilize the structured approach of analysis and power scries ex-pansion to discuss general Fibonacci polynomials and Lucas polynomials, and we obtain some identities. In addition, we also research the general Chebyshev polynomials. The main content contains in this thesis is as follows:1. The study of the summation form like has been made by properties of general Fibonacci polynomials and Lucas poly-nomials.2. We define form like to study identities connect-ing Ln2(x,y) with Bernoulli polynomials and Euler polynomials.3. Some existing conclusions have been generalized by studying identities connecting Fk2(x,y)Lk2(x,y)4. Based on the other literatures and analysis theory, these identities above can been generalized in other polynomials like Chcbyshev polynomials.