Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions

被引：23
作者：
Guo, Bai-Ni [1 ]
Qi, Feng [2 ]
Srivastava, H. M. [3 ]
机构：
[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China
[2] Tianjin Polytech Univ, Coll Sci, Dept Math, Tianjin 300160, Peoples R China
[3] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
来源：
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2010年 / 21卷 / 11期
关键词：
gamma and psi functions; uniqueness results; complete monotonicity; Bernstein-Widder theorem; polygamma functions; square of a polygamma function; Hurwitz (or generalized) zeta function; Riemann zeta function; GAMMA FUNCTIONS; PSI FUNCTIONS;
D O I：
10.1080/10652461003748112
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let the function fm, n(x) be given by [image omitted] In the present paper, we use two markedly different methods in order to prove that, among all fm, n(x)(m, n), only f1, 2(x) is non-trivially completely monotonic on (0, ). More precisely, the functions f1, 2(x) and fm, 2n-1(x) are completely monotonic on (0, ), but the functions fm, 2n(x) for (m, n)(1, 1) are not monotonic and do not keep the same sign on (0, ).
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页码：849 / 858
页数：10
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