SHARP INEQUALITIES FOR POLYGAMMA FUNCTIONS

被引：32
作者：
Guo, Bai-Ni [1 ]
Qi, Feng [2 ]
Zhao, Jiao-Lian [3 ]
Luo, Qiu-Ming [4 ]
机构：
[1] Henan Polytechn Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China
[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China
[3] Weinan Teachers Univ, Dept Math & Informat, Weinan City 714000, Shaanxi Prov, Peoples R China
[4] Chongqing Normal Univ, Dept Math, Chongqing 401331, Peoples R China
来源：
MATHEMATICA SLOVACA | 2015年 / 65卷 / 01期
关键词：
inequality; polygamma function; psi function; completely monotonic function; logarithmically completely monotonic function; TRI-GAMMA FUNCTIONS; MONOTONIC FUNCTIONS; DIVIDED DIFFERENCES; PSI; LOGARITHM; CONVEXITY; PROPERTY; DIGAMMA; BOUNDS; RATIO;
D O I：
10.1515/ms-2015-0010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper, the authors review some inequalities and the (logarithmically) complete monotonicity concerning the gamma and polygamma functions and, more importantly, present a sharp double inequality for bounding the polygamma function by rational functions. (C) 2015 Mathematical Institute Slovak Academy of Sciences
引用
收藏
页码：103 / 120
页数：18
相关论文
共 73 条
[11]  
[Anonymous], 2004, RGMIA RES REP COLL
[12]  
[Anonymous], 1956, Edinb. Math. Notes
[13]  
ATANASSOV RD, 1988, DOKL BOLG AKAD NAUK, V41, P21
[14]  
Batir N., 2005, J INEQUAL PURE APPL, V6, P1
[15]   On some properties of digamma and polygamma functions [J].
Batir, Necdet .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 328 (01) :452-465
[16]   Inequalities for the gamma function [J].
Batir, Necdet .
ARCHIV DER MATHEMATIK, 2008, 91 (06) :554-563
[17]   Logarithmically completely monotonic functions relating to the gamma function [J].
Chen, Chao-Ping ;
Qi, Feng .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 321 (01) :405-411
[18]   THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS [J].
Chu, Yuming ;
Zhang, Xiaoming ;
Zhang, Zhihua .
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 25 (03) :373-383
[19]  
Chu YM, 2008, BULL INST MATH ACAD, V3, P373
[20]   The best bounds in Gautschi's inequality [J].
Elezovic, N ;
Giordano, C ;
Pecaric, J .
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2000, 3 (02) :239-252
12345678