Evaluating residues and integrals through negative dimensional integration method (NDIM)

• Autor(a) principal: Suzuki, Alfredo Takashi [UNESP]
• Data de Publicação: 2006
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://www.actaphys.uj.edu.pl/_cur/store/vol37/pdf/v37p2767.pdf; http://hdl.handle.net/11449/69149
• topic: Algebraic equations; Cauchy's theorem; Gaussian integration; Negative dimensional integration method (NDIM); Integration; Linear algebra; Linear equations; Poles and zeros; Theorem proving; Integral equations

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.