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, ).

引用

页码：849 / 858

页数：10