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Entropy 2017, 19(5), 215; doi:10.3390/e19050215

Cauchy Principal Value Contour Integral with Applications

1
EINA-Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza 50018, Spain
2
CITG-Departamento de Matemática Aplicada, Universitat Politècnica de València, Valencia 46022, Spain
*
Author to whom correspondence should be addressed.
Academic Editors: Carlo Cattani and Kevin Knuth
Received: 28 March 2017 / Revised: 28 April 2017 / Accepted: 3 May 2017 / Published: 10 May 2017
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
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Abstract

Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity. On the other hand, entropy prediction of systems behavior from a thermodynamic perspective commonly involves contour integrals. With the aim of facilitating the calculus of such integrals in this entropic scenario, we revisit the generalization of Cauchy principal value to complex contour integral, formalize its definition and—by using residue theory techniques—provide an useful way to evaluate them. View Full-Text
Keywords: Cauchy principal value; contour integral; entropy as measurement; information extraction; thermodynamics; aerodynamics Cauchy principal value; contour integral; entropy as measurement; information extraction; thermodynamics; aerodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Legua, M.; Sánchez-Ruiz, L.M. Cauchy Principal Value Contour Integral with Applications. Entropy 2017, 19, 215.

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