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

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.

21 pages

References in corpus (3)

• Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions
• Properties of three functions relating to the exponential function and the existence of partitions of unity
• Complete monotonicity of a difference between the exponential and trigamma functions

Cited by in corpus (12)

• Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind
• Derivatives of tangent function and tangent numbers
• Explicit expressions for a family of Bell polynomials and derivatives of some functions
• A logarithmically completely monotonic function involving the ratio of gamma functions
• Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions
• Completely monotonic degree of a function involving the tri- and tetra-gamma functions
• From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
• Some Bernstein functions and integral representations concerning harmonic and geometric means
• Integral representations and properties of some functions involving the logarithmic function
• Some integral representations and properties of Lah numbers
• Complete monotonicity of a difference between the exponential and trigamma functions
• Some inequalities for the trigamma function in terms of the digamma function