Complete monotonicity of a function involving the divided difference of digamma functions

被引：24
作者：
Qi Feng [1 ]
Luo QiuMing [2 ]
Guo BaiNi [1 ]
机构：
[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454010, Peoples R China
[2] Chongqing Normal Univ, Dept Math, Chongqing 401331, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 11期
关键词：
necessary and sufficient condition; completely monotonic function; logarithmically completely monotonic function; divided difference; psi function; inequality for sums; bound for the ratio of two gamma functions; GAMMA FUNCTIONS; POLYGAMMA FUNCTIONS; PROPERTY;
D O I：
10.1007/s11425-012-4562-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.
引用
收藏
页码：2315 / 2325
页数：11
相关论文
共 20 条
  • [1] [Anonymous], 1965, NATL BUR STANDARDS
  • [2] [Anonymous], 1946, PRINCETON MATH SERIE
  • [3] [Anonymous], 2004, Mediterr. J. Math, DOI DOI 10.1007/S00009-004-0022-6
  • [4] [Anonymous], CLASSICAL NEW INEQUA
  • [5] ATANASSOV RD, 1988, DOKL BOLG AKAD NAUK, V41, P21
  • [6] Logarithmically completely monotonic functions relating to the gamma function
    Chen, Chao-Ping
    Qi, Feng
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 321 (01) : 405 - 411
  • [7] Completely monotonic functions involving the gamma and q-gamma functions
    Grinshpan, AZ
    Ismail, MEH
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (04) : 1153 - 1160
  • [8] Guo BN, 2010, U POLITEH BUCH SER A, V72, P21
  • [9] Some completely monotonic functions involving the gamma and polygamma functions
    Qi, F
    Guo, BN
    Chen, CP
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2006, 80 : 81 - 88
  • [10] Some completely monotonic functions involving polygamma functions and an application
    Qi, F
    Cui, RQ
    Chen, CP
    Guo, BN
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 310 (01) : 303 - 308
12