›› 2016, Vol. 35 ›› Issue (4): 26-26.

• 著者文摘 • 上一篇    下一篇

留数定理计算无穷求和及其推广

周运清;黄文涛;周恺元   

  1. 浙江省海洋大数据挖掘与应用重点实验室;浙江海洋学院物理系,浙江舟山316000
  • 出版日期:2016-04-20 发布日期:2016-04-20

Evaluation of infinite sum by residue theorem and its generalization

  • Online:2016-04-20 Published:2016-04-20

摘要: 先讨论了留数定理在某些无穷项级数求和问题中的应用,然后推广至含正弦或余弦三角函数的无穷项级数求和,并作了严格证明,最后举例中两种方法对比说明结果的正确性,及说明留数定理在简化无穷级数时的有效性.

关键词: 留数定理, 无穷项级数求和, 三角函数

Abstract: We discuss the method of summation of some infinite series by the residue theorem,then extend to infinite series containing trigonometric function and give rigorous proofs. Finally,we illustrate the correctness of the present results and compare the result of an example by using two different methods. From an example,we see the effectiveness of residue theorem in the simplification of infinite series.

Key words: residue theorem, sum of infinite series, trigonometric function

中图分类号: 

  • O411