Extension and application of residue theorem

Hanze Guan

doi:10.1117/12.2672676

28 March 2023 Extension and application of residue theorem

Hanze Guan

Proceedings Volume 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022); 125970Z (2023) https://doi.org/10.1117/12.2672676
Event: Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2022, Nanjing, China

Abstract

In learning complex analysis, the residue theorem is the easiest thing to touch. Then in higher mathematics, these concepts are often very abstract, and all exist in graphics. Therefore, the author summarizes the practical application of the residue theorem with reference to other papers. There are many application directions. The simplest and practical application is in generalized integral. This paper introduces the research study topic of the application of generalized residue theorem in Laplace Inverse transform. The application methods and skills of generalized residue theorem in Laplace Inverse transform are discussed in detail through concrete examples. Based on the teaching process of Laplace transformation in mathematical analysis, differential equation or mathematical equation, and the problems and puzzles in the application of Laplace transformation, this paper presents a research-based learning theme. In this paper on the application of residue theorem to series, a new method of summation of infinite series is given based on residue theorem. In this method, the sum of series is transformed into the sum of residues of a complex valued function in a closed domain.

Citation Download Citation

Hanze Guan "Extension and application of residue theorem", Proc. SPIE 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 125970Z (28 March 2023); https://doi.org/10.1117/12.2672676

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