A lower bound for the beta function

Abstract

We present a new lower bound for Euler's beta function, $B(x,y)$, which states that the inequality \begin{equation*} B(x,y)>\frac{x+y}{xy}\left(1-\frac{2xy}{x+y+1}\right) \end{equation*} holds on $(0,1]\times (0,1]$, which improves a lower bound obtained by P. Ivády [12, Theorem, (3.2)] in the case of $0<x+y<1$.