Supplements to a class of logarithmically completely monotonic functions associated with the gamma function

Abstract

Abstract. In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on (0, ∞). As applications of the necessary and sufficient condition, some inequalities for bounding the psi and polygamma functions and the ratio of two gamma functions are derived. This is a continuator of the paper [12].

Some monotonicity properties and inequalities for the (p, k)-gamma function

“…Remark 2.9. The right side of (2.2) and the left side of (2.4) are however weaker than the results obtained in [5,Theorem 3].…”

Complete monotonicity results for some functions involving the gamma and polygamma functions

“…In the recent past a lot of papers appeared providing inequalities and complete monotonicity results for the gamma and related functions; see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and the references therein. In this paper we are concerned with the function…”

Sharp Inequalities for Polygamma Functions

“…For more information on further investigation of functions similar to (1.16), please refer to the research papers [30,32,33,68], the expository article [45] and related references therein.…”