{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:27:24Z","timestamp":1760146044347,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:00:00Z","timestamp":1726272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying the Choi\u2013Srivastava theorem, we reduce these trigonometric series to expressions over Hurwitz\u2019s zeta function derivative.<\/jats:p>","DOI":"10.3390\/axioms13090631","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T11:36:37Z","timestamp":1726486597000},"page":"631","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Closed Forms of Some Trigonometric Series"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3766-8579","authenticated-orcid":false,"given":"Slobodan B.","family":"Tri\u010dkovi\u0107","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Ni\u0161, 18000 Ni\u0161, Serbia"}]},{"given":"Miomir S.","family":"Stankovi\u0107","sequence":"additional","affiliation":[{"name":"Mathematical Institute of Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1080\/10652460801936689","article-title":"On the summation of trigonometric series","volume":"19","year":"2008","journal-title":"Int. Trans. Spec. Func."},{"key":"ref_2","unstructured":"Abramowitz, M., and Stegun, A. (2010). Handbook of Mathematical Functions, Cambridge Universiy Press."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Apostol, T.M. (1976). Introduction to Analytic Number Theory, Springer.","DOI":"10.1007\/978-1-4757-5579-4"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Olver, F.W.J. (1997). Asymptotics and Special Functions, A K Peters.","DOI":"10.1201\/9781439864548"},{"key":"ref_5","unstructured":"Bateman, H., and Erd\u00e9lyi, A. (1953). Higher Transcendental Functions Volume I, McGraw-Hill Book Company, Inc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"417","DOI":"10.32917\/hmj\/1151007490","article-title":"A certain family of series associated with the Zeta and related functions","volume":"32","author":"Choi","year":"2002","journal-title":"Hiroshima Math. J."},{"key":"ref_7","unstructured":"Titchmarsh, E.C. (1986). The Theory of the Riemann Zeta-Function, Clarendon Press."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/9\/631\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:56:37Z","timestamp":1760111797000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/9\/631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,14]]},"references-count":7,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["axioms13090631"],"URL":"https:\/\/doi.org\/10.3390\/axioms13090631","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,9,14]]}}}