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17 May 2022 Cauchy’s residue theorem for a class of real integrals
Zheng Tan, Pengfei Wang, Xiaoying Wang
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Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 122591I (2022) https://doi.org/10.1117/12.2639470
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 2022, Kunming, China
Abstract
Residue theorem is a powerful tool in complex analysis to compute difficult real definite integrals. In this paper, with the help of special auxiliary functions, we’re going to use residue theorem to transform the calculation of real integrals into the calculation of residue. Moreover, we obtain a rather universal approach to solve this kind of problem. Finally, we apply this approach to reckon some specific infinite integrals and derive a special condition for a class of real integrals to be zero.
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Zheng Tan, Pengfei Wang, and Xiaoying Wang "Cauchy’s residue theorem for a class of real integrals", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 122591I (17 May 2022); https://doi.org/10.1117/12.2639470
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KEYWORDS
Integration
Mathematics
Bessel functions
Differential equations
Physics
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