摘要
令L_n(x)为Laguerre多项式,即L_0(x)=1,L_1(x)=-x+1,且对所有整数n≥1,有递推公式L_(n+1)(x)=(2n+1-x)L_n(x)-n^2L_(n-1)(x).主要使用组合及初等方法研究一类包含L_n(x)的卷积和式,给出其有趣的计算公式,并得到一些包含Laguerre多项式的等式和同余式,这些结果均有着重要的应用.
Let L_n(x) denotes the Laguerre polynomials.That is,L_0(x) = 1,L_1(x) =- x +1,and the recurrence formula L_(n+1)(x) =(2n + 1- x)L_n(x)- n^2L_(n-1)(x) for all integers n ≥1.In this paper,we using some combinational skill and elementary methods to study the calculating problem of one kind convolution sums involving L_n(x),and give some interesting computational formulae for it.As some applications of our results,we obtained some new identities and congruences involving the Laguerre polynomials.
作者
祁兰
呼家源
QI Lan HU Jia-yuan(College of Mathematics and Statistics, Yulin University, Yulin 719000, China School of Mathematics, Northwest University, Xi'an 710127, China)
出处
《数学的实践与认识》
北大核心
2016年第19期259-265,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(11371291)
陕西省自然科学基金重点项目(2013JK0889)
陕西省教育厅专项科研项目(16JK1895)