The Study Of The Identities Involving Derivative Of Some Polynomials

Fibonacci polynomial,Lucas polynomial,and two kinds of Chebyshev polynomial is the basis of the second order linear recursive formula of polynomial,Leon from 1202 that Fibonacci the Fibonacci sequence is put forward to now,the Fibonacci polynomial has been being number theory subject widely concerned by experts and scholars,so far,and the Fibonacci polynomials with similar recursive nature of Lucas polynomial and two types of Chebyshev polynomial has become the key research topics in the recursive polynomial.Product of this paper is a continuation of the last century polynomial and all kinds of polynomial of the relationship between research,further to the Fibonacci,Lucas polynomial derivative are studied,through the commonly used integral transform in number theory,trigonometric functions and so on elementary method to calculate,by Fibonacci,Lucas and the orthogonality of the two types of Chebyshev polynomial is also calculated to prove lemma,provides the proof of theorem of great help.Second chapter because Lucas polynomial derivative can be written as the product of the number and the Fibonacci polynomials,simple structure,according to the previous related research literature,to further expand to the derivative of polynomial Lucas level,mainly through the orthogonality of the polynomial and deformation of binomial expansion method formula,which several theorems are obtained.The third chapter mainly introduces the relations between Fibonacci and two kinds of Chebyshev polynomials and the higher derivatives of Lucas polynomials,USES other polynomials to express the higher derivatives of Lucas polynomials,obtains the relevant lemma through integral transformation and other methods,and completes the theorem proof.