Some inequalities for the growth of elliptic integrals

被引：20

作者：

Qiu, SL ^{[1
]}

Vamanamurthy, MK

Vuorinen, M

机构：

[1] Hangzhou Inst Elect Engn, Sch Sci & Arts, Hangzhou 310037, Peoples R China

[2] Univ Auckland, Dept Math, Auckland, New Zealand

[3] Univ Helsinki, Dept Math, FIN-00014 Helsinki, Finland

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1998年 / 29卷 / 05期

关键词：

concave; convex; elliptic integrals; modulus; ring;

D O I：

10.1137/S0036141096310491

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Growth of the complete elliptic integral K (r) near the singularity r = 1 is studied and new bounds in terms of elementary functions are obtained. In particular, two recent conjectures are solved and various convexity properties of K(r) are given.

引用

页码：1224 / 1237

页数：14

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