{"title":"Wallis序列的渐近展开式及与Glaisher-Kinkelin和Choi-Srivastava常数相关的一些新的数学常数","authors":"Xue Han, Chao-Ping Chen, H. Srivastava","doi":"10.2298/aadm220414024h","DOIUrl":null,"url":null,"abstract":"The celebrated Wallis sequence Wn, which is defined by Wn := ?nk=1 4k2/4k2?1, is known to have the limit ? 2 as n ? ?. Without using the Bernoulli numbers Bn, the authors present several asymptotic expansions and a recurrence relation for determining the coefficients of each asymptotic expansion related to the Wallis sequence Wn and the newly-introduced constants D and E, which are analogous to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants\",\"authors\":\"Xue Han, Chao-Ping Chen, H. Srivastava\",\"doi\":\"10.2298/aadm220414024h\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The celebrated Wallis sequence Wn, which is defined by Wn := ?nk=1 4k2/4k2?1, is known to have the limit ? 2 as n ? ?. Without using the Bernoulli numbers Bn, the authors present several asymptotic expansions and a recurrence relation for determining the coefficients of each asymptotic expansion related to the Wallis sequence Wn and the newly-introduced constants D and E, which are analogous to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C.\",\"PeriodicalId\":51232,\"journal\":{\"name\":\"Applicable Analysis and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Analysis and Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2298/aadm220414024h\",\"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":"100","ListUrlMain":"https://doi.org/10.2298/aadm220414024h","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants
The celebrated Wallis sequence Wn, which is defined by Wn := ?nk=1 4k2/4k2?1, is known to have the limit ? 2 as n ? ?. Without using the Bernoulli numbers Bn, the authors present several asymptotic expansions and a recurrence relation for determining the coefficients of each asymptotic expansion related to the Wallis sequence Wn and the newly-introduced constants D and E, which are analogous to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C.
期刊介绍：
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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