{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T07:03:13Z","timestamp":1784617393287,"version":"3.55.0"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,10]],"date-time":"2017-05-10T00:00:00Z","timestamp":1494374400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2014by using residue theory techniques\u2014provide an useful way to evaluate them.<\/jats:p>","DOI":"10.3390\/e19050215","type":"journal-article","created":{"date-parts":[[2017,5,10]],"date-time":"2017-05-10T12:04:20Z","timestamp":1494417860000},"page":"215","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Cauchy Principal Value Contour Integral with Applications"],"prefix":"10.3390","volume":"19","author":[{"given":"Matilde","family":"Legua","sequence":"first","affiliation":[{"name":"EINA-Departamento de Matem\u00e1tica Aplicada, Universidad de Zaragoza, Zaragoza 50018, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7559-6724","authenticated-orcid":false,"given":"Luis","family":"S\u00e1nchez-Ruiz","sequence":"additional","affiliation":[{"name":"CITG-Departamento de Matem\u00e1tica Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia 46022, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,10]]},"reference":[{"key":"ref_1","unstructured":"Cover, T.M., and Thomas, J.A. 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