Residues of Complex Functions with Definite and Infinite Poles on X-axis
Abbas Y. AL-Bayati and Sasan A. Al-Shwani
DOI : 10.3844/jmssp.2009.152.158
Journal of Mathematics and Statistics
Volume 5, 2009
Problem statement: One of the most popular areas in the mathematics is the computational complex analysis. In this study several computational complex techniques were investigated and implemented numerically. Objective: This study produced new procedures to compute the residues of complex functions by changing their numerator from a constant number to either even or odd function. Approach: In this project we studied the functions that had finite and infinite poles Zi, i greater than one of order greater or equal one, also we found new relation between residues at the poles Zi and residues at the poles -Zi, i greater than one and we had used these relations to solve improper integrals of this type. The project needed the knowledge of computing the complex improper integrations. Results: Our numerical results in computing the residues for improper integrals of definite and infinite poles on the x-axis were well defined. Conclusion: In this study, we had concluded that the residues of the complex functions had definite and infinite poles of higher order with constant numerator. A general form of residues of these functions of high orders were also investigated.
© 2009 Abbas Y. AL-Bayati and Sasan A. Al-Shwani. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.