Interdisciplinary Application of Residue Theorem in Trigonometric and Fraction Functions

Yeheng Xiao

2025

Abstract

In complex function theory, there exists a fundamental concept known as the residue theorem., lies at the intersection of pure mathematics and diverse scientific applications. This theorem elegantly connects the integrand function over a precisely defined closed geometric contour in the complex plane to the sum of its residues at isolated singularities within that contour. In mathematics, it serves as a potent means for the evaluation of otherwise intractable complex integrals, offering new insights into the behavior of complex valued functions, from analyzing the distribution of zeros and poles to studying function singularities. Its applications span multiple scientific disciplines. In physics, it simplifies calculations in quantum mechanics, electromagnetism, and statistical physics, providing crucial solutions for problems like scattering amplitudes and electromagnetic field distributions. In engineering, it aids in signal processing and control system design, especially when dealing with Laplace and Fourier transforms. Hence, this paper aims to calculate representative definite integrals with the help of Residue theorem, paving the way for connecting its applications in interdisciplinary field.

Paper Citation

in Harvard Style

Xiao Y. (2025). Interdisciplinary Application of Residue Theorem in Trigonometric and Fraction Functions. In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA; ISBN 978-989-758-774-0, SciTePress, pages 109-113. DOI: 10.5220/0013814900004708

in Bibtex Style

@conference{iampa25,
author={Yeheng Xiao},
title={Interdisciplinary Application of Residue Theorem in Trigonometric and Fraction Functions},
booktitle={Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA},
year={2025},
pages={109-113},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013814900004708},
isbn={978-989-758-774-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA
TI - Interdisciplinary Application of Residue Theorem in Trigonometric and Fraction Functions
SN - 978-989-758-774-0
AU - Xiao Y.
PY - 2025
SP - 109
EP - 113
DO - 10.5220/0013814900004708
PB - SciTePress