Abstract. In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two gamma functions to be logarithmically completely monotonic, and some double inequalities are deduced for bounding divided differences of polygamma functions. 1.

Abstract. In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized. 1.

Abstract. In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel’s, Gurland’s, Kazarinoff’s, Gautschi’s, Watson’s, Chu’s, Lazarević-Lupa¸s’s, Kershaw’s and Elezović-Giordano-Pečarić’s inequalities, claim, monotonic and convex properties. On the other hand, we introduce some related advances on the topic of bounding the ratio of two gamma functions in recent years. Contents

Abstract. In the present note, an alternative proof is supplied for Theorem 1

Abstract. Let Ωn stand for the volume of the unit ball in Rn for n ∈ N. In the 1/(n ln n) present paper, we prove that the sequence Ωn is logarithmically convex 1/(n ln n) Ω and that the sequence is strictly decreasing for n ≥ 2. In n Ω 1/[(n+1)ln(n+1)] n+1 addition, some monotonic and concave properties of several functions relating to Ωn are extended and generalized.

Abstract. The main aim of this paper is to prove that the double inequality

Abstract. In the note, the functions ˛ ˛ψ (i) (e x) ˛ ˛ for i ∈ N are proved to be sub-additive on (ln θi, ∞) and super-additive on (−∞,ln θi), where θi ∈ (0, 1) is the unique root of equation 2 ˛ ˛ ψ (i) (θ)

Abstract. In the paper, some lower bounds for polygamma functions are refined. 1. Introduction and