{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:59:37Z","timestamp":1760151577043,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T00:00:00Z","timestamp":1648944000000},"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","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>Closed expressions for a number of septuple integrals involving the product of three Bessel functions of the first kind J\u03b1(t\u03b2)J\u03b3(x\u03b4)J\u03b7(y\u03b8) when the orders \u03b1,\u03b3,\u03b7 are large, are derived in terms of the Hurwitz\u2013Lerch zeta function \u03a6(z,s,v). The integrals are not easy to to evaluate for complex values of the parameters. All the results in this work are new.<\/jats:p>","DOI":"10.3390\/sym14040730","type":"journal-article","created":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T06:04:01Z","timestamp":1648965841000},"page":"730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Septuple Integral of the Product of Three Bessel Functions of the First Kind J\u03b1(t\u03b2)J\u03b3(x\u03b4)J\u03b7(y\u03b8): Derivation and Evaluation over General Indices"],"prefix":"10.3390","volume":"14","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, 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, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1137\/0503043","article-title":"Integrals of products of Bessel functions","volume":"3","author":"Jackson","year":"1972","journal-title":"SIAM J. 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Polylogarithms and Associated Functions, North-Holland Publishing Co."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/730\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:49:18Z","timestamp":1760136558000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/4\/730"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,3]]},"references-count":12,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["sym14040730"],"URL":"https:\/\/doi.org\/10.3390\/sym14040730","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,4,3]]}}}