Some inequalities for the ratio of gamma functions

被引：4
作者：
Cao, Xiaodong [1 ]
Wang, Ruopeng [1 ]
机构：
[1] Beijing Inst Petrochem Technol, Dept Math & Phys, Beijing 102617, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年
基金：
中国国家自然科学基金;
关键词：
gamma function; Wallis ratio; inequalities; continued fraction; rate of convergence; MULTIPLE-CORRECTION; APPROXIMATION; FORMULAS;
D O I：
10.1186/s13660-015-0701-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present some sharp inequalities for the ratio of gamma functions. The main tool is the multiple-correction method formulated in (Cao et al. in J. Number Theory 149: 327-350, 2015; Cao in J. Math. Anal. Appl. 424: 1425-1446, 2015). Some conjectures are proposed.
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页数：11
相关论文
共 26 条
  • [1] Abramowitz M., 1972, APPL MATH SERIES, V55
  • [2] Berndt B. C., 1997, Ramanujan's Notebooks
  • [3] Multiple-correction and continued fraction approximation
    Cao, Xiaodong
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 424 (02) : 1425 - 1446
  • [4] Multiple-correction and faster approximation
    Cao, Xiaodong
    Xu, Hongmin
    You, Xu
    [J]. JOURNAL OF NUMBER THEORY, 2015, 149 : 327 - 350
  • [5] New sequence converging towards the Euler-Mascheroni constant
    Chen, Chao-Ping
    Mortici, Cristinel
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (04) : 391 - 398
  • [6] Chen CP, 2005, TAMKANG J MATH, V36, P303
  • [7] The best bounds in Wallis' inequality
    Chen, CP
    Qi, F
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (02) : 397 - 401
  • [8] SHARP INEQUALITIES FOR POLYGAMMA FUNCTIONS
    Guo, Bai-Ni
    Qi, Feng
    Zhao, Jiao-Lian
    Luo, Qiu-Ming
    [J]. MATHEMATICA SLOVACA, 2015, 65 (01) : 103 - 120
  • [9] Some exact constants for the approximation of the quantity in the Wallis' formula
    Guo, Senlin
    Xu, Jian-Guo
    Qi, Feng
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [10] On irrationality exponents of generalized continued fractions
    Hancl, Jaroslav
    Leppala, Kalle
    Matala-aho, Tapani
    Torma, Topi
    [J]. JOURNAL OF NUMBER THEORY, 2015, 151 : 18 - 35
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