一类多重级数求和的组合方法  

A Combinatorial Summation Method for a Class of Multiple Series

作　　者：张祥德[1] 唐青松[1] 朱和贵[1] 杨连平[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2010年第7期1061-1064,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(50704012)

摘　　要：Rao和Subbarao用复杂的初等方法给出了一个三重级数的变换公式,本文利用组合数学方法,结合Bell多项式及Stirling数,给出了一类基于Riemann-Zeta函数的多重级数变换公式的简短证明.利用该变换公式,不仅可以得到Rao和Subbarao等人的经典结论作为特例,而且给出了一些新的结果.Rao and Subbarao gave a transformation formula of triple series by complicated elementary operation. Based on the combinatorial method, the Bell polynomials are combined with Stirling number to give a brief proof to the transformation formula for a class of multiple series based on Riemann-Zeta function. The formula is available to not only get the classical conclusions offered by Rao and Subarao as particular cases, but also give some near findings.

关 键 词：多重级数 组合方法 BELL多项式 STIRLING数 

分 类 号：O157.1[理学—数学]