Ai-Jun Li

SOME COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND POLYGAMMA FUNCTIONS

The function [Γ(x+1)]1/x x ( 1 + 1 x )x is strictly logarithmically completely monotonic in (0,∞). The function ψ′′(x + 2) + 1+x 2 x2(1+x)2 is strictly completely monotonic in (0,∞).

AN EXTENDED LOOMIS–WHITNEY INEQUALITY FOR POSITIVE DOUBLE JOHN BASES

In this paper, we establish an extended Loomis-Whitney inequality for positive double John bases, which generalises Balls result (1). Moreover, a different extension of the Loomis-Whitney inequality is deduced.