BOUNDS FOR THE RATIO OF TWO GAMMA FUNCTIONS-FROM WENDEL'S AND RELATED INEQUALITIES TO LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS

被引：50
|
作者：
Qi, Feng [2 ]
Luo, Qiu-Ming [1 ]
机构：
[1] Chongqing Normal Univ, Dept Math, Chongqing 401331, Peoples R China
[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2012年 / 6卷 / 02期
关键词：
Bound; ratio of two gamma functions; logarithmically completely monotonic function; gamma function; q-gamma function; DIVIDED DIFFERENCES; PSI; EXTENSIONS; PROPERTY;
D O I：
10.15352/bjma/1342210165
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the survey paper, along one of several main lines of bounding the ratio of two gamma functions, the authors retrospect and analyse Wendel's double inequality, Kazarinoff's refinement of Wallis' formula, Watson's monotonicity, Gautschi's double inequality, Kershaw's first double inequality, and the (logarithmically) complete monotonicity results of functions involving ratios of two gamma or q-gamma functions obtained by Bustoz, Ismail, Lorch, Muldoon, and other mathematicians.
引用
收藏
页码：132 / 158
页数：27
相关论文
共 50 条
  • [1] Wendel's and Gautschi's inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions
    Qi, Feng
    Guo, Bai-Ni
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 205 (01) : 281 - 290
  • [2] A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS
    Qi, Feng
    Li, Wen-Hui
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2015, 5 (04): : 626 - 634
  • [3] SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION
    Qi, Feng
    Guo, Bai-Ni
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 47 (06) : 1283 - 1297
  • [4] Two logarithmically completely monotonic functions connected with gamma function
    Qi, Feng
    Yang, Qiao
    Li, Wei
    [J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2006, 17 (07) : 539 - 542
  • [5] Logarithmically completely monotonic functions concerning gamma and digamma functions
    Qi, Feng
    Chen, Shou-Xin
    Cheung, Wing-Sum
    [J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2007, 18 (06) : 435 - 443
  • [6] A class of logarithmically completely monotonic functions related to the gamma function with applications
    Guo, Senlin
    Qi, Feng
    Srivastava, H. M.
    [J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2012, 23 (08) : 557 - 566
  • [7] Some Properties of Functions Related to Certain Classes of Completely Monotonic Functions and Logarithmically Completely Monotonic Functions
    Guo, Senlin
    Srivastava, H. M.
    Cheung, Wing-Sum
    [J]. FILOMAT, 2014, 28 (04) : 821 - 828
  • [8] TWO CLASSES OF LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS ASSOCIATED WITH THE GAMMA FUNCTION
    Chen, Chaoping
    Wang, Gang
    Zhu, Hua
    [J]. COMPUTATIONAL INTELLIGENCE: FOUNDATIONS AND APPLICATIONS: PROCEEDINGS OF THE 9TH INTERNATIONAL FLINS CONFERENCE, 2010, 4 : 168 - +
  • [9] 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
  • [10] COMPLETELY MONOTONIC FUNCTIONS RELATED TO GURLAND'S RATIO FOR THE GAMMA FUNCTION
    Chen, Chao-Ping
    Choi, Junesang
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (03): : 651 - 659
12345