{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:28:50Z","timestamp":1760236130336,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T00:00:00Z","timestamp":1635379200000},"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","504070"],"award-info":[{"award-number":["504070","504070"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We derive a new formula for the Hurwitz\u2013Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.<\/jats:p>","DOI":"10.3390\/axioms10040279","type":"journal-article","created":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T23:50:28Z","timestamp":1635465028000},"page":"279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Series Representation for the Hurwitz\u2013Lerch Zeta Function"],"prefix":"10.3390","volume":"10","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":[[2021,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/BF02612318","article-title":"Note sur la fonction Re(w,x,s) = \u2211k=0\u221ee2k\u03c0ix(w+k)s","volume":"11","author":"Lerch","year":"1887","journal-title":"Acta Math."},{"unstructured":"Erd\u00e9yli, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1953). Higher Transcendental Functions, McGraw-Hill Book Company, Inc.","key":"ref_2"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s11139-007-9102-0","article-title":"Double integrals and infinite products for some classical constants via analytic continuations of Lerch\u2019s transcendent","volume":"16","author":"Guillera","year":"2008","journal-title":"Ramanujan J."},{"unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Digital Library of Mathematical Functions, With 1 CD-ROM (Windows, Macintosh and UNIX). MR 2723248 (2012a:33001).","key":"ref_4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"235","DOI":"10.12988\/imf.2020.91272","article-title":"A Method for Evaluating Definite Integrals in Terms of Special Functions with Examples","volume":"15","author":"Reynolds","year":"2020","journal-title":"Int. Math. Forum"},{"doi-asserted-by":"crossref","unstructured":"Choi, J., \u015eahin, R., Ya\u011fc\u0131, O., and Kim, D. (2020). Note on the Hurwitz\u2013Lerch Zeta Function of Two Variables. Symmetry, 12.","key":"ref_6","DOI":"10.3390\/sym12091431"},{"doi-asserted-by":"crossref","unstructured":"Laurin\u010dikas, A., and Garunk\u0161tis, R. (2002). The Lerch Zeta-Function, Kluwer.","key":"ref_7","DOI":"10.1007\/978-94-017-6401-8"},{"unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2000). Tables of Integrals, Series and Products, Academic Press. [6th ed.].","key":"ref_8"},{"unstructured":"Prudnikov, A.P., Brychkov, I.A., and Marichev, O.I. (1990). Integrals and Series, More Special Functions, USSR Academy of Sciences.","key":"ref_9"},{"doi-asserted-by":"crossref","unstructured":"Oldham, K.B., Myland, J., and Spanier, J. (2009). An Atlas of Functions: With Equator, the Atlas Function Calculator, Springer.","key":"ref_10","DOI":"10.1007\/978-0-387-48807-3"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/279\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:21:45Z","timestamp":1760167305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/279"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,28]]},"references-count":10,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["axioms10040279"],"URL":"https:\/\/doi.org\/10.3390\/axioms10040279","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,10,28]]}}}