Next Article in Journal
On the Convergence and Law of Large Numbers for the Non-Euclidean Lp -Means
Next Article in Special Issue
A Novel Distance Metric: Generalized Relative Entropy
Previous Article in Journal
Meromorphic Non-Integrability of Several 3D Dynamical Systems
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(5), 215;

Cauchy Principal Value Contour Integral with Applications

EINA-Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza 50018, Spain
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)
View Full-Text   |   Download PDF [278 KB, uploaded 11 May 2017]


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).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top