东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2010, Vol. 31 ›› Issue (7): 1061-1064.DOI: -

• 论著 • 上一篇    

一类多重级数求和的组合方法

张祥德;唐青松;朱和贵;杨连平;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-20 修回日期:2013-06-20 出版日期:2010-07-15 发布日期:2013-06-20
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(50704012)

A combinatorial summation method for a class of multiple series

Zhang, Xiang-De (1); Tang, Qing-Song (1); Zhu, He-Gui (1); Yang, Lian-Ping (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China
  • Received:2013-06-20 Revised:2013-06-20 Online:2010-07-15 Published:2013-06-20
  • Contact: Tang, Q.-S.
  • About author:-
  • Supported by:
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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.

关键词: 多重级数, 组合方法, Bell多项式, Stirling数

Abstract: 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.

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