Monotonicity properties and bounds for the complete p-elliptic integrals

被引:61
作者
Huang, Ti-Ren [1 ]
Tan, Shen-Yang [2 ]
Ma, Xiao-Yan [1 ]
Chu, Yu-Ming [3 ]
机构
[1] Zhejiang Sci Tech Univ, Dept Math, Hangzhou, Zhejiang, Peoples R China
[2] Nanjing Univ Sci & Technol, Taizhou Inst Sci & Technol, Taizhou, Peoples R China
[3] Huzhou Univ, Dept Math, Huzhou, Peoples R China
关键词
Complete elliptic integral; Complete p-elliptic integral; Gaussian hypergeometric function; Monotonicity; Convexity; INEQUALITIES; CONVEXITY;
D O I
10.1186/s13660-018-1828-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
引用
收藏
页数:11
相关论文
共 35 条
[1]  
Alzer H, 2015, ANAL MATH, V41, P133, DOI 10.1007/s10476-015-0201-7
[2]   Elliptic integral inequalities, with applications [J].
Anderson, GD ;
Qiu, SL ;
Vamanamurthy, MK .
CONSTRUCTIVE APPROXIMATION, 1998, 14 (02) :195-207
[3]   Generalized elliptic integrals and modular equations [J].
Anderson, GD ;
Qiu, SL ;
Vamanamurthy, MK ;
Vuorinen, M .
PACIFIC JOURNAL OF MATHEMATICS, 2000, 192 (01) :1-37
[4]  
Anderson GD, 1997, CONFORMAL INVARINANT
[5]  
[Anonymous], 1948, Handbook of Mathematical Functions withFormulas, Graphs, and Mathematical Tables, DOI DOI 10.1119/1.15378
[6]  
[Anonymous], 1987, PI AGM STUDY ANAL NU
[7]   ON GENERALIZED COMPLETE ELLIPTIC INTEGRALS AND MODULAR FUNCTIONS [J].
Bhayo, B. A. ;
Vuorinen, M. .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2012, 55 :591-611
[8]   REMARKS ON GENERALIZED TRIGONOMETRIC FUNCTIONS [J].
Bushell, P. J. ;
Edmunds, D. E. .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2012, 42 (01) :25-57
[9]  
Byrd P., 1971, Grundlehren der mathematischen Wissenschaften
[10]   Sharp Generalized Seiffert Mean Bounds for Toader Mean [J].
Chu, Yu-Ming ;
Wang, Miao-Kun ;
Qiu, Song-Liang ;
Qiu, Ye-Fang .
ABSTRACT AND APPLIED ANALYSIS, 2011,