Monotonicity theorems and inequalities for the complete elliptic integrals\

被引：189

作者：

Alzer, H ^{[1
]}

Qiu, SL ^{[1
]}

机构：

[1] Hangzhou Inst Elect Engn, Presidents Off, Hangzhou 310037, Zhejiang, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2004年 / 172卷 / 02期

基金：

芬兰科学院;

关键词：

complete elliptic integrals; monotonicity; inequalities; mean values; Arc length of an ellipse;

D O I：

10.1016/j.cam.2004.02.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, K and E. These results lead to sharp symmetrical bounds for K and E, which improve recently discovered inequalities. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：289 / 312

页数：24

共 44 条

[31] THE LOGARITHMIC MEAN IN N-VARIABLES [J].

PITTENGER, AO .

AMERICAN MATHEMATICAL MONTHLY, 1985, 92 (02) :99-104

[32] Asymptotic expansions and inequalities for hypergeometric functions [J].

Ponnusamy, S ;

Vuorinen, M .

MATHEMATIKA, 1997, 44 (88) :278-301

[33]

Qiu S. L., 1992, ACTA MATH SINICA, V35, P492

[34]

QiU S.-L., 1996, COMPLEX VARIABLES TH, V30, P77

[35] Some inequalities for the growth of elliptic integrals [J].

Qiu, SL ;

Vamanamurthy, MK ;

Vuorinen, M .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1998, 29 (05) :1224-1237

[36] Sharp estimates for complete elliptic integrals [J].

Qiu, SL ;

Vamanamurthy, MK .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1996, 27 (03) :823-834

[37]

Qiu SL., 1995, PANAMER MATH J, V5, P41

[38]

QIU SL, 1997, J HANGZHOU I ELECT E, V3, P1

[39] ON CERTAIN INEQUALITIES FOR MEANS [J].

SANDOR, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 189 (02) :602-606

[40] On certain inequalities for means .2. [J].

Sandor, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 199 (02) :629-635

← 1 2 3 4 5 →