{"title":"On closed forms of some trigonometric series","authors":"Slobodan B. Tričković, Miomir S. Stanković","doi":"arxiv-2407.12885","DOIUrl":null,"url":null,"abstract":"We have derived alternative closed-form formulas for the trigonometric series\nover sine or cosine functions when the immediate replacement of the parameter\nappearing in the denominator with a positive integer gives rise to a\nsingularity. By applying the Choi-Srivastava theorem, we reduce these\ntrigonometric series to expressions over Hurwitz's zeta function derivative.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.12885","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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-Srivastava theorem, we reduce these
trigonometric series to expressions over Hurwitz's zeta function derivative.
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