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2008•Journal of Huanggang Normal UniversityRequires access

A note on the residue theorem

Mingquan Li

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Abstract

Objective: To calculate the complex integral.Methods: To employ the basic theory in complex functions.Results: Cauchy-Goursat theorem,Cauchy integral formula,and the higher derivative formula of the analytic function are all the special case of the residue theorem.Those complex integrals,which can be calculated by Cauchy-Goursat theorem,Cauchy integral formula,and the higher derivative formula of the analytic function,can all be calculated by the residue theorem.Conclusion: The research plays a significant role in application.

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What this paper is about

Objective: To calculate the complex integral.Methods: To employ the basic theory in complex functions.Results: Cauchy-Goursat theorem,Cauchy integral formula,and the higher derivative formula of the analytic function are all the special case of the residue theorem.Those complex integrals,which can be calculated by Cauchy-Goursat theorem,Cauchy integral formula,and the higher derivative formula of the analytic function,can all be calculated by the residue theorem.Conclusion: The research plays a significant role in application.

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Available abstract

Objective: To calculate the complex integral.Methods: To employ the basic theory in complex functions.Results: Cauchy-Goursat theorem,Cauchy integral formula,and the higher derivative formula of the analytic function are all the special case of the residue theorem.Those complex integrals,which can be calculated by Cauchy-Goursat theorem,Cauchy integral formula,and the higher derivative formula of the analytic function,can all be calculated by the residue theorem.Conclusion: The research plays a significant role in application.

Key concepts: Residue theorem, Cauchy's integral formula, Mathematics, Cauchy's integral theorem, Cauchy distribution, Residue (chemistry), Analytic function, Pure mathematics

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