{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:26:48Z","timestamp":1760236008379,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T00:00:00Z","timestamp":1634688000000},"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 object of this paper is to derive a double integral in terms of the Hurwitz\u2013Lerch zeta function. Almost all Hurwitz\u2013Lerch zeta functions have an asymmetrical zero-distribution. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.<\/jats:p>","DOI":"10.3390\/sym13111983","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T22:07:04Z","timestamp":1634767624000},"page":"1983","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Double Logarithmic Transform Involving the Exponential and Polynomial Functions Expressed in Terms of the Hurwitz\u2013Lerch Zeta 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, 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":[[2021,10,20]]},"reference":[{"key":"ref_1","unstructured":"Simon, P., and De Laplace, M. (1820). Th\u00e9orie Analytique des Probabilit\u00e9s, Courcier."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Poularikas, A.D. (2000). The Transforms and Applications Handbook, CRC Press LLC. [2nd ed.].","DOI":"10.1201\/9781420036756"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s40819-015-0057-3","article-title":"The Double Laplace Transforms and Their Properties with Applications to Functional, Integral and Partial Differential Equations","volume":"2","author":"Debnath","year":"2016","journal-title":"Int. J. Appl. Comput. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1016\/j.jmaa.2014.09.015","article-title":"The pricing of vulnerable options with double Mellin transforms","volume":"422","author":"Yoon","year":"2015","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Finch, S.R. (2003). f Mathematical Constants, Cambridge University Press.","DOI":"10.1017\/CBO9780511550447"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2144","DOI":"10.1137\/17M1154217","article-title":"Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles","volume":"50","author":"Bennett","year":"2018","journal-title":"SIAM J. Math. Anal."},{"key":"ref_7","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"},{"key":"ref_8","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2000). Tables of Integrals, Series and Products, Academic Press. [6th ed.]."},{"key":"ref_9","unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Digital Library of Mathematical Functions, Cambridge University Press. With 1 CD-ROM (Windows, Macintosh and UNIX). MR 2723248 (2012a:33001)."},{"key":"ref_10","first-page":"234","article-title":"Some general families of the Hurwitz-Lerch Zeta functions and their applications: Recent developments and directions for further researches","volume":"45","author":"Srivastava","year":"2019","journal-title":"Proc. Inst. Math. Mech. Nat. Acad. Sci. Azerbaijan"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"329","DOI":"10.25073\/jaec.201931.229","article-title":"The Zeta and Related Functions: Recent Developments","volume":"3","author":"Srivastava","year":"2019","journal-title":"J. Adv. Eng. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Oldham, K.B., Myland, J.C., and Spanier, J. (2009). An Atlas of Functions: With Equator, the Atlas Function Calculator, Springer. [2nd ed.].","DOI":"10.1007\/978-0-387-48807-3"},{"key":"ref_13","unstructured":"Marichev, O., Sondow, J., and Weisstein, E.W. (2021, September 01). Catalan\u2019s Constant, From MathWorld\u2013A Wolfram Web Resource. Available online: https:\/\/mathworld.wolfram.com\/CatalansConstant.html."},{"key":"ref_14","unstructured":"Weisstein, E.W. (2021, September 01). Lerch Transcendent, From MathWorld\u2013A Wolfram Web Resource. Available online: https:\/\/mathworld.wolfram.com\/LerchTranscendent.html."},{"key":"ref_15","unstructured":"Reese, S., and Sondow, J. (2021, September 01). Universal Parabolic Constant, From MathWorld\u2013A Wolfram Web Resource, created by Eric W. Weisstein. Available online: https:\/\/mathworld.wolfram.com\/UniversalParabolicConstant.html."},{"key":"ref_16","unstructured":"Sondow, J., and Weisstein, E.W. (2021, September 01). Riemann Zeta Function, From MathWorld\u2013A Wolfram Web Resource. Available online: https:\/\/mathworld.wolfram.com\/RiemannZetaFunction.html."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/1983\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:19:02Z","timestamp":1760167142000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/11\/1983"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,20]]},"references-count":16,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["sym13111983"],"URL":"https:\/\/doi.org\/10.3390\/sym13111983","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,10,20]]}}}