A class of strongly completely monotonic functions related to gamma function

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:367

Article

Zhu, Ling¹ 

[1] Zhejiang Gongshang Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

关键词: Strongly completely monotonic function;    Completely monotonic function;    Gamma function;   

DOI  :  10.1016/j.cam.2019.112469

来源: Elsevier

【 摘 要 】

A function f : (0, infinity)-> R is called strongly completely monotonic if it has derivatives of all orders and (-1)(n)x(n+1)f((n))(X) is nonnegative and decreasing on (0, infinity) for all n >= 0. In this paper, we prove the function g(n)(x) =in Gamma (x + 1/2) - x in x + x - 1/2 in (2 pi) + Sigma(n)(k=1) (1-2(1-2k))( )B-2k/2k(2k-1) x(2k-1) is strongly completely monotonic on (0, infinity). Using the same technique, we give an alternative proof of a known result. Moreover, two conjectures are proposed. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free