大学物理 ›› 2020, Vol. 39 ›› Issue (9): 31-33.doi: 10.16854 /j.cnki.1000-0712.190431
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邱为钢
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QIU Wei-gang
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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
邱为钢. 无穷求和与留数定理[J]. 大学物理, 2020, 39(9): 31-33.
QIU Wei-gang. Infinite sum and residue theorem[J]. College Physics, 2020, 39(9): 31-33.
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链接本文: https://dxwl.bnu.edu.cn/CN/10.16854 /j.cnki.1000-0712.190431
https://dxwl.bnu.edu.cn/CN/Y2020/V39/I9/31
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