Closed solution to partial fraction expansion
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Keywords
Rational Function, Partial Fraction, Recursive Solution, Field of Functions
Abstract
The present work pretends to set forth a general methodology,
applicable to the study of rational functions.
In the field R[C], of rational functions over the complex field, we provide a recursive formula that gives closed
form solution to the problem of separating a rational
function into its elementary functions. The solution to
the coefficients of the partial fraction expansion can
be calculated recursively in terms of combinatorics
and elementary operations of complex numbers. We
deal with specific cases that are studied for the comprehension
of the general method, which is used in
the last section to find the general formula.
References
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Polia, G. (1989). Como plantear y resolver problemas. México, D: F: Trillas
Dr. Konrad Knopp (1945) Theory of Functions. Part One: Elements of the General Theory of Analytic Functions. New York, Dover Publications.
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William Enrique Londoño Terwes, University of Guadalajara
Department of Mathematics. University Center of the North, CUNorte, University of Guadalajara
Juan Pablo Ramírez Ramírez, University of Guadalajara
University Center of the North, CUNorte, University of Guadalajara
Guillermo Aguilar Herver, University of Guadalajara
Master in generation and management of innovation University Center of the North, CUNorte, University of Guadalajara.
Javier Ramírez Romo, University of Guadalajara
University Center of the North, CUNorte, University of Guadalajara
Imelda Karina Salinas Ocegueda, University of Guadalajara
University Center of the North, CUNorte, University of Guadalajara