{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:34:06Z","timestamp":1760402046269,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,7]],"date-time":"2022-01-07T00:00:00Z","timestamp":1641513600000},"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>The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The zero distribution of almost all Hurwitz-Lerch zeta functions is asymmetrical. All the results in this work are new.<\/jats:p>","DOI":"10.3390\/sym14010100","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Quadruple Integral Involving Chebyshev Polynomials Tn(x): Derivation and Evaluation"],"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":[[2022,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Oldham, K.B., Myland, J.C., and Spanier, J. 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Tables of Integrals, Series and Products, Academic Press. [6th ed.]."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Harrison, M., and Waldron, P. (2011). Mathematics for Economics and Finance, Taylor & Francis.","DOI":"10.4324\/9780203829998"},{"key":"ref_12","unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Digital Library of Mathematical Functions."},{"key":"ref_13","unstructured":"Laurincikas, A., and Garunkstis, R. (2013). The Lerch Zeta-Function, Springer Science & Business Media."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/1\/100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:27:03Z","timestamp":1760362023000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/1\/100"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,7]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["sym14010100"],"URL":"https:\/\/doi.org\/10.3390\/sym14010100","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,1,7]]}}}