Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions

Feng Qi, Shu-Hong Wang

Published 2012-10-07, updated 2012-10-12Version 2

In the paper, the authors verify the complete monotonicity of the difference $e^{1/t}-\psi'(t)$ on $(0,\infty)$, compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of $e^{1/z}$, and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind.