A class of completely monotonic functions involving the gamma and polygamma functions

被引：4
作者：
Guo, Bai-Ni [1 ]
Qi, Feng [2 ,3 ]
机构：
[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454010, Henan, Peoples R China
[2] Inner Mongolia Univ Natl, Coll Math, Inner Mongolia Autonomous Reg, Tongliao 028043, Peoples R China
[3] Tianjin Polytechn Univ, Coll Sci, Dept Math, Tianjin 300387, Peoples R China
来源：
COGENT MATHEMATICS | 2014年 / 1卷
基金：
中国国家自然科学基金;
关键词：
complete monotonicity; gamma function; polygamma function;
D O I：
10.1080/23311835.2014.982896
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper the authors show that neither the function In Gamma(x) - (x - 1/2) In x + x - 1/2In x+x - 1/2In(2 pi) -a(1)[-1)(i+1)psi((l))(x+b(l))] nor its negative is completely monotonic on (0, infinity), where a i >= 0 and b i = 0 are real numbers, i >= 2, Gamma(x) is the classical Euler's gamma function, and psi((i))(x) = [Gamma(x)/Gamma(x)]((i)) are polygamma functions. Moreover, some other results are given in the form of remarks.
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页数：7
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