无穷求和与留数定理  

Infinite sum and residue theorem

作　　者：邱为钢 QIU Wei-gang(Qiuzhen School,Huzhou Teacher s College,Huzhou,Jiangsu 313000,China)

机构地区：[1]湖州师范学院求真学院,浙江湖州313000

出　　处：《大学物理》2020年第9期31-33,共3页College Physics

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.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.

关 键 词：无穷求和 留数定理 超越方程 

分 类 号：O174.5[理学—数学]