Analysis of the Residue Theorem and Its Applications


  • Yuntong Li



Residue theorem; Definite integral; Logarithmic residue; Complex analysis.


Residue theorem is a useful tool for studying complex variable function. Residue theorem can be widely used in various disciplines, and it helps people solve a lot of practical problems. The residue theorem plays an important role in both mathematics and physics. It can not only make integral easier, but also solve problems that related to thermodynamics, optics, and electricity. In practice, it is usually complicated to solve the definite integral by using substitution, partial integration method and so on. Although these methods can calculate the solution, the computational workload is too large and complex. Using residue theorem to transform integral formulas can help people solve integrals easily. The method of using the residue theorem to solve the integral is more convenient than some traditional methods. In this paper, some applications of residue theorem are introduced. Further, it also gives some examples for calculating the integral by using residue theorem and logarithmic residue theorem.


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How to Cite

Li, Y. (2024). Analysis of the Residue Theorem and Its Applications. Highlights in Science, Engineering and Technology, 88, 439-444.