ANZIAM J. 44(2003), 609–623 INEQUALITIES FOR THE BETA FUNCTION OF n VARIABLES

We present various inequalities for Euler’s beta function of n variables. One of our theorems states that the inequalities an 1Qn iD1 xi − B.x1; : : : ; xn / bn () hold for all xi 1 (i D 1; : : : ; n; n 3) with the best possible constants an D 0 and bn D 1 − 1=.n − 1/W. This extends a recently published result of Dragomir et al., who investigated () for the special case n D 2. 1