关于Lucas多项式的一些恒等式

Some Identities Involving Lucas Polynomials

目的研究Lucas多项式与Lucas数的乘积和的计算公式.方法初等方法和解析方法.结果得到了一类关于Lucas多项式的恒等式,作为应用,给出了关于Lucas数乘积和的几个恒等式.结论研究方法可用于研究其他特殊多项式,如第二类Chebyshev等特殊多项式,所得结果将对Lucas多项式的研究和应用起到积极作用.

Aim To study the identities of the summations of multiple products on Lucas polynomials and Lucas numbers.Methods Elementary method and Analytic method.Restdts Some identities involving Lucas polynomials are obtained,as an application,several identities on Lucas numbers are given.Conclusion The methods could be used in other researching on special functions,such as studying the second Chebyshev polynomials.It is sure that the results we obtained in this paper will play an role in the research of Lucas polynomials and its applications.