一组关于Fibonacci数列及Lucas数列的恒等式  

Some identities involving Fibonacci sequence and Lucas sequence

作　　者：陈国慧[1] CHEN Guohui(College of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China)

机构地区：[1]海南师范大学数学与统计学院

出　　处：《纺织高校基础科学学报》2019年第3期289-292,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11771351);海南省自然科学基金(118MS041)

摘　　要：针对一些包含二阶线性递推数列和式的计算问题,根据Fibonacci多项式以及Lucas多形式的定义和性质,在已有研究结果的基础上,利用初等方法以及指数函数的幂级数展开,给出了包含这些二阶线性数列的若干新的计算公式。对所得结果进行分析和推广,得到了一系列有趣的恒等式。There exists the summation problem about the convolution sums of second-order linear recursion sequences.Given the definition and properties of Fibonacci and Lucas polynomials, based on the existing research results,by using the elementary method and the power series expansion of exponential function,some new calculation formulas of these second-order linear recursion sequence are obtained.In addition,by analyzing and generalizing these new results, a series of interesting identities are obtained.

关 键 词：二阶线性递推数列 求和问题 恒等式 初等方法 

分 类 号：O156.7[理学—数学]