{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:11:06Z","timestamp":1777367466252,"version":"3.51.4"},"reference-count":12,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T00:00:00Z","timestamp":1630886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["504070"],"award-info":[{"award-number":["504070"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A quadruple integral involving the logarithmic, exponential and polynomial functions is derived in terms of the Lerch function. Special cases of this integral are evaluated in terms of special functions and fundamental constants. Almost all Lerch functions have an asymmetrical zero-distribution. The majority of the results in this work are new.<\/jats:p>","DOI":"10.3390\/sym13091638","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T23:55:22Z","timestamp":1630972522000},"page":"1638","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Quadruple Definite Integral Expressed in Terms of the Lerch Function"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4230-9925","authenticated-orcid":false,"given":"Robert","family":"Reynolds","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7252-5004","authenticated-orcid":false,"given":"Allan","family":"Stauffer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0377-0427(90)90369-B","article-title":"Asymptotic expansion of a quadruple integral involving a Bessel function","volume":"33","author":"McClure","year":"1990","journal-title":"J. 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[2nd ed.].","DOI":"10.1007\/978-0-387-48807-3"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1638\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:57:20Z","timestamp":1760165840000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1638"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,6]]},"references-count":12,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["sym13091638"],"URL":"https:\/\/doi.org\/10.3390\/sym13091638","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,6]]}}}