{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T08:25:40Z","timestamp":1762071940497,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T00:00:00Z","timestamp":1666742400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The problem of computing the Laplace transform of composed functions has not found its way into the literature because it was customarily believed that there were no suitable formula to solve it. Actually, it has been shown in previous work that by making use of Bell polynomials, efficient approximations can be found. Moreover, using an extension of Bell\u2019s polynomials to bivariate functions, it is also possible to approximate the Laplace transform of composed functions of two variables. This topic is solved in this paper and some numerical verifications, due to the first author using the computer algebra system Mathematica\u00a9, are given proving the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/axioms11110591","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T07:17:48Z","timestamp":1666768668000},"page":"591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Laplace Transform of Composed Functions and Bivariate Bell Polynomials"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0969-884X","authenticated-orcid":false,"given":"Diego","family":"Caratelli","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7581-615X","authenticated-orcid":false,"given":"Rekha","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7899-3087","authenticated-orcid":false,"given":"Paolo Emilio","family":"Ricci","sequence":"additional","affiliation":[{"name":"Department of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,26]]},"reference":[{"key":"ref_1","first-page":"1501","article-title":"Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformations","volume":"22","author":"Srivastava","year":"2021","journal-title":"J. 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Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel Publishing Co.","DOI":"10.1007\/978-94-010-2196-8"},{"key":"ref_7","unstructured":"Fa\u00e0 di Bruno, F. (1876). Th\u00e9orie des Formes Binaires, Brero."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"124382","DOI":"10.1016\/j.jmaa.2020.124382","article-title":"Special values of the Bell polynomials of the second kind for some sequences and functions","volume":"491","author":"Qi","year":"2020","journal-title":"J. Math. Anal. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1080\/00029890.1980.11995156","article-title":"The Fa\u00e0 di Bruno Formula","volume":"87","author":"Roman","year":"1980","journal-title":"Amer. Math. Monthly"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0001-8708(78)90087-7","article-title":"The umbral calculus","volume":"27","author":"Roman","year":"1978","journal-title":"Adv. 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Wiley & Sons."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/591\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:03:10Z","timestamp":1760144590000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/591"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,26]]},"references-count":19,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["axioms11110591"],"URL":"https:\/\/doi.org\/10.3390\/axioms11110591","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,10,26]]}}}