Open AccessResidues of Complex Functions with Definite and Infinite Poles on X-axis
Author(s) -
Abbas Y. Al-Bayati,
Sasan A. Al-Shwani
Publication year - 2009
Publication title -
journal of mathematics and statistics
Language(s) - English
Resource type - Journals
eISSN - 1558-6359
pISSN - 1549-3644
DOI - 10.3844/jmssp.2009.152.158
Subject(s) - mathematics , positive definite matrix , pure mathematics , combinatorics , mathematical analysis , eigenvalues and eigenvectors , quantum mechanics , physics
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