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

Abstract

In the paper, the authors verify the complete monotonicity of the difference $e^{1/t}-{\psi }^{\prime }(t)$ 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.

6 pages

References in corpus (5)

• Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
• An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions
• Properties of three functions relating to the exponential function and the existence of partitions of unity
• Some integral representations and properties of Lah numbers
• Complete monotonicity of a difference between the exponential and trigamma functions

Cited by in corpus (14)

• 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
• Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
• Completely monotonic degree of a function involving the tri- and tetra-gamma functions
• An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions
• An explicit formula for computing Bell numbers in terms of Lah and Stirling numbers
• 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