Monotonicity and inequalities for the gamma function

被引：49
|
作者：
Yang, Zhen-Hang [1 ,2 ]
Tian, Jing-Feng [1 ]
机构：
[1] North China Elect Power Univ, Coll Sci & Technol, Ruixiang St 282, Baoding 071051, Peoples R China
[2] State Grid Zhejiang Elect Power Co, Res Inst, Dept Sci & Technol, Hangzhou 310014, Zhejiang, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年
关键词：
gamma function; Laplace transform; complete monotonicity; inequality; ASYMPTOTIC FORMULAS; FACTORIAL FUNCTION; BURNSIDES FORMULA; SERIES; APPROXIMATION;
D O I：
10.1186/s13660-017-1591-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x bar right arrow 1/24x(In Gamma(x + 1/2) - x In x + x - In root 2 pi) + 1 - 120/7 x(2) is strictly increasing from (0,infinity) onto (1, 1860/343). This not only yields some known and new inequalities for the gamma function, but also gives some completely monotonic functions related to the gamma function.
引用
收藏
页数：15
相关论文
共 50 条
  • [1] Monotonicity and inequalities for the gamma function
    Zhen-Hang Yang
    Jing-Feng Tian
    Journal of Inequalities and Applications, 2017
  • [2] Inequalities and monotonicity properties for the gamma function
    Giordano, C
    Laforgia, A
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) : 387 - 396
  • [3] MONOTONICITY AND INEQUALITIES INVOLVING THE INCOMPLETE GAMMA FUNCTION
    Lv, Hui-Lin
    Yang, Zhen-Hang
    Zheng, Shenzhou
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2019, 13 (02): : 351 - 367
  • [4] MONOTONICITY THEOREMS AND INEQUALITIES FOR THE GAMMA FUNCTION
    Kupan, Pal A.
    Szasz, Robert
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2014, 17 (01): : 149 - 159
  • [5] Monotonicity and inequalities involving the incomplete gamma function
    Yang, Zhen-Hang
    Zhang, Wen
    Chu, Yu-Ming
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
  • [6] MONOTONICITY AND SHARP INEQUALITIES RELATED TO GAMMA FUNCTION
    Yang, Zhen-Hang
    Tian, Jingfeng
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2018, 12 (01): : 1 - 22
  • [7] SOME MONOTONICITY PROPERTIES AND INEQUALITIES FOR THE (p,k)-GAMMA FUNCTION
    Nantomah, Kwara
    Merovci, Faton
    Nasiru, Suleman
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2018, 42 (02): : 287 - 297
  • [8] Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function
    Chen, Chao-Ping
    APPLIED MATHEMATICS AND COMPUTATION, 2016, 283 : 385 - 396
  • [9] Monotonicity and inequalities involving the incomplete gamma function
    Zhen-Hang Yang
    Wen Zhang
    Yu-Ming Chu
    Journal of Inequalities and Applications, 2016
  • [10] Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function
    Yang, Zhen-Hang
    Tian, Jing-Feng
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (04) : 3603 - 3617
12345