Completely monotonic degrees for a difference between the logarithmic and psi functions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:361

Article

Qi, Feng^1,2,3  Liu, Ai-Qi⁴ 

[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China

[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao 028043, Inner Mongolia, Peoples R China

[3] Tianjin Polytech Univ, Sch Math Sci, Tianjin 300387, Peoples R China

[4] Sanmenxia Polytech, Dept Math, Sanmenxia 472000, Henan, Peoples R China

关键词: Completely monotonic degree;    Psi function;    Logarithmic function;    Asymptotic formula;    Remainder;    Conjecture;   

DOI  :  10.1016/j.cam.2019.05.001

来源: Elsevier

【 摘 要 】

In the paper, the authors firstly present a concise proof for complete monotonicity of a function involving a difference between the logarithmic and psi functions, secondly compute completely monotonic degree of the above-mentioned function, and finally pose several conjectures on completely monotonic degrees of remainders and their derivatives for the asymptotic formula of the logarithm of the classical Euler gamma function. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free