Asymptotic Expansions for Large Degree Tangent and Apostol-Tangent Polynomials of Complex Order

J. Appl. Math. Pub Date : 2023-06-24 DOI:10.1155/2023/9917885

C. Corcino, R. Corcino, Jeremar Casquejo

{"title":"Asymptotic Expansions for Large Degree Tangent and Apostol-Tangent Polynomials of Complex Order","authors":"C. Corcino, R. Corcino, Jeremar Casquejo","doi":"10.1155/2023/9917885","DOIUrl":null,"url":null,"abstract":"This paper provides asymptotic expansions for large values of \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>n</mi>\n </math>\n of tangent \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <msubsup>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n <mrow>\n <mi>μ</mi>\n </mrow>\n </msubsup>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>z</mi>\n </mrow>\n </mfenced>\n </math>\n and Apostol-tangent \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msubsup>\n <mrow>\n <mi>T</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n <mrow>\n <mi>μ</mi>\n </mrow>\n </msubsup>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>z</mi>\n <mo>;</mo>\n <mi>λ</mi>\n </mrow>\n </mfenced>\n </math>\n polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"6 1","pages":"9917885:1-9917885:8"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Appl. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/9917885","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}