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

[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.

[发布日期] 2019-12-01

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