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[1]焦仁兵,裘松良,葛耿韬.广义( p,q )椭圆积分的单调性和凹凸性[J].浙江理工大学学报,2018,39-40(自科6):765-769.
　JIAO Renbing,QIU Songliang,GE Gengtao.Monotonicity and convexity properties of  the generalized ( p,q )elliptic integrals[J].Journal of Zhejiang Sci-Tech University,2018,39-40(自科6):765-769.
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广义( p,q )椭圆积分的单调性和凹凸性()
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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:
765-769
栏目:
出版日期:
2018-11-10

文章信息/Info

Title:
Monotonicity and convexity properties of  the generalized ( p,q )elliptic integrals
文章编号:
1673-3851 (2018) 11-0765-05
作者:
焦仁兵; 裘松良; 葛耿韬
浙江理工大学理学院，杭州 310018
Author(s):
JIAO Renbing;  QIU Songliang;  GE Gengtao
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
广义( p; q)三角函数; 广义(p; q)  椭圆积分; 单调性; 凹凸性
分类号:
O174.6
文献标志码:
A
摘要:
In this paper, the authors obtain several monotonicity and convexity  properties of the generalized ( p,q )elliptic integrals K p,q ( r ) and  E p,q ( r ) for  p,q∈(1,∞) and  r ∈(0,1), by studying the analytic properties of certain combinations in terms of  K p,q ( r ), E p,q ( r ) and some elementary functions.

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 Publications,1966:556-607.
［2］ Drábek P, Manrásevich R. On the closed solution to some pLaplacian nonhomogeneous eigenvalue problems［J］. Differential Integral Equations,1999,12(6):733-788.
［3］ Takeuchi S. Generalized Jacobian elliptic functions and their application to bifurcation problems associates with pLaplacian［J］. Journal of Mathematical Analysis and Applications,2012,385(1):24-35.
［4］ Takeuchi S. Legendretype relations for generalized complete elliptic integrals［J］. Journal of Classical Analysis,2016,9(1):35-42.
［5］ Kamiya T, Takeuchi S. Complete (p,q)elliptic integrals with application to a family of means［J］. Journal of Classical Analysis,2017,10(1):15-25.
［6］ Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps［M］. New York: John Wiley and Sons,1997:48-73.
［7］ Borwein J M, Borwein P B. Pi and the AGM［M］. New York: A WileyInterscience Publication,1987:1-32.
［8］ 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.
［9］ Anderson G D, Vamanamurthy M K, Vuorinen M. Functional inequalities for complete elliptic integrals and their ratios［J］. SIAM Journal on Mathematical Analysis,2012,21(2):536-549.
［10］ Qiu S L, Vamanamurthy M K, Vuorinen M. Some inequalities for the growth of elliptic integrals［J］. SIAM Journal on Mathematical Analysis,2006,29(5):1224-1237.

备注/Memo

备注/Memo:
Received date： 2018-05-29
Published Online： 2018-09-04
Fund item： This research is supported by the NSF of P. R. China (Grant No.11771400)
Introduction of the first anthor： JIAO Renbing(1994-), male, Anqing, Anhui, postgraduate, research interests: quasiconformal theory, special functions, Ramanujans modular equations.
Corresponding author： QIU Songliang, E-mail: sl_qiu@zstu.edu.cn
更新日期/Last Update: 2018-11-14