C. Corcino, R. Corcino, Jeremar Casquejo
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{"title":"复阶大次正切多项式和乘切多项式的渐近展开式","authors":"C. Corcino, R. Corcino, Jeremar Casquejo","doi":"10.1155/2023/9917885","DOIUrl":null,"url":null,"abstract":"<jats:p>This paper provides asymptotic expansions for large values of <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>n</mi>\n </math>\n </jats:inline-formula> of tangent <jats:inline-formula>\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 </jats:inline-formula> and Apostol-tangent <jats:inline-formula>\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 </jats:inline-formula> polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.</jats:p>","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":"{\"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\":\"<jats:p>This paper provides asymptotic expansions for large values of <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>n</mi>\\n </math>\\n </jats:inline-formula> of tangent <jats:inline-formula>\\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 </jats:inline-formula> and Apostol-tangent <jats:inline-formula>\\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 </jats:inline-formula> polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.</jats:p>\",\"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}","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}
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