|本期目录/Table of Contents|

[1]葛耿韬,裘松良,焦仁兵.第一类完全椭圆积分之商的一个双向不等式[J].浙江理工大学学报,2018,39-40(自科6):770-775.
　GE Gengtao,QIU Songliang,JIAO Renbing.A double inequality for the ratio of complete elliptic integrals of the first kind[J].Journal of Zhejiang Sci-Tech University,2018,39-40(自科6):770-775.
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第一类完全椭圆积分之商的一个双向不等式()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第39-40卷
期数:
2018年自科6期
页码:
770-775
栏目:
出版日期:
2018-11-10

文章信息/Info

Title:
A double inequality for the ratio of complete elliptic integrals of the first kind
文章编号:
1673-3851 (2018) 11-0770-06
作者:
葛耿韬; 裘松良; 焦仁兵
浙江理工大学理学院，杭州 310018
Author(s):
GE Gengtao;  QIU Songliang;  JIAO Renbing
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
完全椭圆积分; 单调性; 上下界; 不等式
分类号:
O174.6
文献标志码:
A
摘要:
建立了第一类完全椭圆积分的商K( r )/K(r)所满足的一个双向不等式。该不等式给出的上界小于至今已知的所有上界，而下界的证明则简化了最近由Alzer和Richards给出的证明。

参考文献/References:

［1］ Abramowitz M, Stegun I A. Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables［M］. New York: Dover,1965.
［2］ Andrews G, Askey R, Roy R. Special Functions, Encyclopedia of Mathematics and Its Applications［M］. Cambridge: Cambridge University Press,1999:132-143.
［3］ Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps［M］. New York: John Wiley and Sons,1997:48-73.
［4］ Carlson B C. Special Functions of Applied Mathematics［M］. New York: Academic Press,1977:257-287.
［5］ Anderson G D, Vamanamurthy M K, Vuorinen M. Functional inequalities for hypergeometric functions and complete elliptic integrals［J］. SIAM Journal on Mathematical Analysis,1992,23(2):512-524.
［6］ Qiu S L, Vamanamurthy M K. Sharp estimates for complete elliptic integrals［J］. SIAM Journal on Mathematical Analysis,1996,27(3):823-834.
［7］ Alzer H, Richards K. Inequalities for the ratio of complete elliptic integrals［J］. Proceedings of the American Mathematical Society,2017,145(4):1661-1670.
［8］ Qiu S L,  Vamanamurthy M K, Vuorinen M. Some inequalities for the growth of elliptic integrals［J］. SIAM Journal on Mathematical Analysis,1998,29(5):1224-1237.
［9］ Alzer H, Qiu S L. Monotonicity theorems and inequalities for the complete elliptic integrals ［J］. Journal of Computational and Applied Mathematics,2004,172(2):289-312.
［10］ Chu Y M, Qiu S L, Wang M K. Sharp inequalities involving the power mean and complete elliptic integral of the first kind［J］. Rocky Mountain Journal of Mathematics,2013,43(5):1489-1496.

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备注/Memo

备注/Memo:
Received date： 2018-06-01
Published Online： 2018-09-04
Fund item： The research is supported by NSF of P. R. China (Grant No. 11771400)
Introdu ction of the first anothor： GE Gengtao(1988-), male, Taizhou, master candidate, research interests: special functions.
Corresponding author： QIU Songliang, E-mail: sl_qiu@zstu.edu.cn
更新日期/Last Update: 2018-11-14