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

Feng Qi, Shu-Hong Wang

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 represe…