{"title":"Some results on Arakawa–Kaneko, Kaneko–Tsumura functions and related functions","authors":"Maneka Pallewatta, Ce Xu","doi":"10.1007/s10998-024-00585-2","DOIUrl":null,"url":null,"abstract":"<p>Recently, the level two analogue of the multiple polylogarithm function <span>\\(\\textrm{A}(k_1,\\ldots ,k_r;z)\\)</span> and the Arakawa–Kaneko zeta function <span>\\(\\psi (k_1,\\ldots ,k_r;s)\\)</span> have been introduced by M. Kaneko and H. Tsumura for <span>\\(k_1,\\ldots ,k_r\\in \\mathbb {Z}_{\\ge 1}\\)</span>. In this paper, we investigate some of their special relations. In particular, we prove some explicit forms of <span>\\(\\textrm{A}(k_1,\\ldots ,k_r;z)\\)</span> and <span>\\(\\psi (k_1,\\ldots ,k_r;s)\\)</span>. Also, we introduce a level <i>m</i> analogue of the Arakawa–Kaneko zeta functions.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"86 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Periodica Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00585-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, the level two analogue of the multiple polylogarithm function \(\textrm{A}(k_1,\ldots ,k_r;z)\) and the Arakawa–Kaneko zeta function \(\psi (k_1,\ldots ,k_r;s)\) have been introduced by M. Kaneko and H. Tsumura for \(k_1,\ldots ,k_r\in \mathbb {Z}_{\ge 1}\). In this paper, we investigate some of their special relations. In particular, we prove some explicit forms of \(\textrm{A}(k_1,\ldots ,k_r;z)\) and \(\psi (k_1,\ldots ,k_r;s)\). Also, we introduce a level m analogue of the Arakawa–Kaneko zeta functions.
期刊介绍:
Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica.
Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.