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

TL;DR

This paper investigates properties of special functions, proving complete monotonicity, deriving integral representations, and establishing inequalities related to exponential, trigamma, and modified Bessel functions.

Contribution

It verifies complete monotonicity of a specific function difference, computes its monotonic degree, and derives new integral representations and inequalities for special functions.

Findings

Confirmed complete monotonicity of e^{1/t}-ψ'(t) on (0,∞)

Derived integral representations for the Laurent series remainder of e^{1/z}

Established a lower bound inequality for the modified Bessel function

Abstract

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.