{"title":"与高斯微分函数相关的两个序列的解析和渐近表示","authors":"Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava","doi":"10.2298/aadm220810024h","DOIUrl":null,"url":null,"abstract":"Let the sequences Gn and gn be defined by Gn := ?10 dt/(1?t2n)1/n (n ? 2) and gn := ??0 dt/(1 + t2n)1/n (n ? 1). In this paper, we first derive analytical representations for these two sequences Gn and gn in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for Gn and gn.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical and asymptotic representations for two sequence related to Gauss’ lemniscate functions\",\"authors\":\"Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava\",\"doi\":\"10.2298/aadm220810024h\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let the sequences Gn and gn be defined by Gn := ?10 dt/(1?t2n)1/n (n ? 2) and gn := ??0 dt/(1 + t2n)1/n (n ? 1). In this paper, we first derive analytical representations for these two sequences Gn and gn in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for Gn and gn.\",\"PeriodicalId\":51232,\"journal\":{\"name\":\"Applicable Analysis and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Analysis and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/aadm220810024h\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/aadm220810024h","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Analytical and asymptotic representations for two sequence related to Gauss’ lemniscate functions
Let the sequences Gn and gn be defined by Gn := ?10 dt/(1?t2n)1/n (n ? 2) and gn := ??0 dt/(1 + t2n)1/n (n ? 1). In this paper, we first derive analytical representations for these two sequences Gn and gn in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for Gn and gn.
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Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).
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