完全椭圆积分的渐近展开式和界

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2020-01-01 DOI:10.7153/mia-2020-23-67

Miao-Kun Wang, Y. Chu, Yong-Min Li, E. Zhang

{"title":"完全椭圆积分的渐近展开式和界","authors":"Miao-Kun Wang, Y. Chu, Yong-Min Li, E. Zhang","doi":"10.7153/mia-2020-23-67","DOIUrl":null,"url":null,"abstract":"In the article, we present several new bounds for the the complete elliptic integrals K (r)= ∫ π/2 0 (1−r2 sin2 θ )−1/2dθ and E (r)= ∫ π/2 0 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1 , which are the refinements and improvements of the previously well-known results. Mathematics subject classification (2010): 33E05, 26E60.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"821-841"},"PeriodicalIF":0.9000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":"{\"title\":\"Asymptotic expansion and bounds for complete elliptic integrals\",\"authors\":\"Miao-Kun Wang, Y. Chu, Yong-Min Li, E. Zhang\",\"doi\":\"10.7153/mia-2020-23-67\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the article, we present several new bounds for the the complete elliptic integrals K (r)= ∫ π/2 0 (1−r2 sin2 θ )−1/2dθ and E (r)= ∫ π/2 0 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1 , which are the refinements and improvements of the previously well-known results. Mathematics subject classification (2010): 33E05, 26E60.\",\"PeriodicalId\":49868,\"journal\":{\"name\":\"Mathematical Inequalities & Applications\",\"volume\":\"1 1\",\"pages\":\"821-841\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"29\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Inequalities & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7153/mia-2020-23-67\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Inequalities & Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/mia-2020-23-67","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 29

摘要

本文给出了完整椭圆积分K (r)=∫π/2 0(1−r2 sin2 θ) - 1/2dθ和E (r)=∫π/2 0(1−r2 sin2 θ)1/2dθ的几个新的界，并给出了K (r)在r→1时的渐近展开式，这是对前人已知结果的改进和改进。数学学科分类(2010):33E05, 26E60。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Asymptotic expansion and bounds for complete elliptic integrals

In the article, we present several new bounds for the the complete elliptic integrals K (r)= ∫ π/2 0 (1−r2 sin2 θ )−1/2dθ and E (r)= ∫ π/2 0 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1 , which are the refinements and improvements of the previously well-known results. Mathematics subject classification (2010): 33E05, 26E60.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.