Some complete monotonicity properties for the (p, q)-gamma function

被引:8
作者
Krasniqi, V. B. [1 ]
Srivastava, H. M. [2 ]
Dragomir, S. S. [3 ,4 ]
机构
[1] Univ Prishtina, Dept Math & Comp Sci, Prishtine 10000, Republic Of Kos, Serbia
[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[3] Victoria Univ Technol, Sch Sci & Engn, Sect Math, Melbourne, Vic 8001, Australia
[4] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
关键词
Completely monotonic functions; Logarithmically completely monotonic functions; Log-convex functions; (p; q)-Gamma function; q)-Psi function; Borel measure; Laplace transforms; Young's inequality; GENERALIZED GAMMA; Q-ANALOG; INEQUALITIES; ZETA;
D O I
10.1016/j.amc.2013.04.034
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
For the Gamma(p,q)-function, we derive several properties and characteristics related to convexity, log-convexity and complete monotonicity. Similar properties and characteristics of the corresponding (p, q)-analogue psi(p,q) (x) of the digamma or the psi-function have also been established. By applying the main results in this paper when p -> infinity and q -> 1, we obtain all of the results given in several earlier works by (for example) Krasniqi, Shabani, and other authors. Some potential areas of applications of the results presented in this paper are also indicated. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:10538 / 10547
页数:10
相关论文
共 23 条
[1]   On some inequalities for the gamma and psi functions [J].
Alzer, H .
MATHEMATICS OF COMPUTATION, 1997, 66 (217) :373-389
[2]  
[Anonymous], 2010, Handbook of Mathematical Functions
[3]  
[Anonymous], 1964, NBS APPL MATH SERIES
[4]  
Apostol T.M., 1976, INTRO ANAL NUMBER TH
[5]  
Askey R., 1978, Applicable Anal., V8, P125
[6]  
Bochner S., 1955, HARMONIC ANAL THEORY
[7]   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
[8]   Integral Representations for the Euler-Mascheroni Constant [J].
Choi, Junesang ;
Srivastava, H. M. .
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2010, 21 (09) :675-690
[9]  
ISMAIL MEH, 1994, INT S NUM M, V119, P309
[10]   On a q-analogue of the p-adic log gamma functions and related integrals [J].
Kim, T .
JOURNAL OF NUMBER THEORY, 1999, 76 (02) :320-329