Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions

TL;DR

This paper investigates properties of modified Bessel functions and determines the completely monotonic degrees of differences between exponential and trigamma functions, providing new inequalities and monotonicity results.

Contribution

It establishes inequalities, monotonicity, convexity, and unimodality for functions related to modified Bessel functions and calculates the completely monotonic degrees of specific function differences.

Findings

Established inequalities and monotonicity properties for Bessel-related functions

Computed the completely monotonic degrees of exponential and trigamma differences

Analyzed convexity and unimodality of the functions involved

Abstract

In the paper, the author establishes inequalities, monotonicity, convexity, and unimodality for functions concerning the modified Bessel functions of the first kind and compute the completely monotonic degrees of differences between the exponential and trigamma functions.