大学物理 ›› 2020, Vol. 39 ›› Issue (9): 31-33.doi: 10.16854 /j.cnki.1000-0712.190431

• 教学讨论 • 上一篇    下一篇

无穷求和与留数定理

邱为钢   

  1. 湖州师范学院求真学院,浙江湖州313000
  • 收稿日期:2019-09-25 修回日期:2020-02-11 出版日期:2020-09-20 发布日期:2020-09-24
  • 作者简介:邱为钢( 1975—) ,男,江苏张家港人,湖州师范学院理学院副教授,博士,主要从事大学数学物理教学研究工作.

Infinite sum and residue theorem

QIU Wei-gang   

  1. Qiuzhen School,Huzhou Teachers College,Huzhou,Jiangsu 313000,China
  • Received:2019-09-25 Revised:2020-02-11 Online:2020-09-20 Published:2020-09-24

摘要: 复变函数在无穷远处围道上的积分值趋近于另一复变函数的积分值.应用留数定理,得到了一类对超越方程所有根无穷求和的解析表达式.数值计算验证了解析表达式的正确性.

关键词: 无穷求和, 留数定理, 超越方程

Abstract: The contour integral of a complex function on an infinite square is approximately the same as another

complex function. The analytical expression of infinite summation of all the zeroes of some transcendental equation is

derived by residue theorem,which is verified by the numerical calculation.

Key words: infinite sum, residue theorem, transcendental equation