A comparison theorem for two divided differences and applications to special functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Yang, Zhenhang¹  Tian, Jing-Feng¹ 

[1] North China Elect Power Univ, Coll Sci & Technol, Baoding 071051, Hebei, Peoples R China

关键词: Comparison theorem;    Completely monotonic function;    Gamma function;    Psi function;    Polygamma function;    Functional inequality;   

DOI  :  10.1016/j.jmaa.2018.04.024

来源: Elsevier

【 摘 要 】

In this paper, we present a general comparison theorem for two divided differences of a three times differentiable function. This gives a unified treatment for (logarithmically) complete monotonicity, monotonicity and inequalities involving some special functions including gamma, psi and polygamma functions. As their consequences, we not only refine and generalize some important results, but also present simple and interesting alternative proofs of certain earlier results. (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free