Complete monotonicity of a difference between the exponential and trigamma functions

Abstract

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi }^{\prime }(t)$ on $(0,\infty )$.

4 pages

References in corpus (2)

• Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions
• Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions

Cited by in corpus (5)

• 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
• Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
• From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
• Some inequalities for the trigamma function in terms of the digamma function