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

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.Comment: 21 page

A Completely Monotonic Function Involving Divided Difference of Psi Function and an Equivalent Inequality Involving Sum

In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sum are founded, and an equivalent relation between the complete monotonicity and one of the class of inequalities is established

Jordan's Inequality: Refinements, Generalizations, Applications and Related Problems

This is an expository article. Some developments on refinements, generalizations, applications of Jordan’s inequality and related problems, including some estimates for three classes of complete elliptic integrals and several proofs of Wilker’s inequality, are summarized

Diagonal recurrence relations for the Stirling numbers of the first kind

In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.Comment: 7 page

Properties of three functions relating to the exponential function and the existence of partitions of unity

In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete monotonicity, logarithmically complete monotonicity, absolute monotonicity, and the like.Comment: 5 page