{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:23:22Z","timestamp":1760235802539,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T00:00:00Z","timestamp":1632960000000},"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>This is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. A summary table of the results are produced for easy reading. A vast majority of the results are new.<\/jats:p>","DOI":"10.3390\/sym13101828","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1828","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Note on a Fourier Sine Transform"],"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":[[2021,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Berndt, B.C. 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Forum"},{"key":"ref_9","unstructured":"Gradshteyn, I.S., and Ryzhik, I.M. (2000). Tables of Integrals, Series and Products, Academic Press. [6th ed.]."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Brychkov, Y.A., Marichev, O.I., and Savischenko, N.V. (2018). Handbook of Mellin Transforms, Chapman and Hall\/CRC. [1st ed.].","DOI":"10.1201\/9780429434259"},{"key":"ref_11","unstructured":"Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Digital Library of Mathematical Functions."},{"key":"ref_12","unstructured":"Erd\u00e9yli, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1953). Higher Transcendental Functions, McGraw-Hill Book Company, Inc."},{"key":"ref_13","unstructured":"Abramowitz, M., and Stegun, I.A. (1982). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover. [9th ed.]."},{"key":"ref_14","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_15","first-page":"2001","article-title":"On the Degree Sequence of Random Geometric Digraphs","volume":"4","author":"Shang","year":"2010","journal-title":"Appl. Math. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1828\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:08:10Z","timestamp":1760166490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1828"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,30]]},"references-count":15,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101828"],"URL":"https:\/\/doi.org\/10.3390\/sym13101828","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,9,30]]}}}