Inequalities for the beta function of n variables

Abstract

AbstractWe present various inequalities for Euler's beta function of n variables. One of our theorems states that the inequalitieshold for all xi ≥ (i = 1,… n; n ≥ 3) with the best possible constants an = 0 and bn = 1 − 1/(n − 1)!. This extends a recently published result of Dragomir et al., who investigated (*) for the special case n = 2.