{"title":"Sharp weighted Hölder mean bounds for the complete elliptic integral of the second kind","authors":"Miao-Kun Wang, Zai-Yin He, Tie-hong Zhao, Qi Bao","doi":"10.1080/10652469.2022.2155819","DOIUrl":null,"url":null,"abstract":"ABSTRACT This paper deals with the complete integral of the second kind approximated by the weighted Hölder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Hölder mean bounds for in a sense of weight. As a result, we also provide a new method to find the optimal Hölder mean bounds for .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"537 - 551"},"PeriodicalIF":0.7000,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Transforms and Special Functions","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10652469.2022.2155819","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
ABSTRACT This paper deals with the complete integral of the second kind approximated by the weighted Hölder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Hölder mean bounds for in a sense of weight. As a result, we also provide a new method to find the optimal Hölder mean bounds for .
期刊介绍：
Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.
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