A lower bound for the beta function

Tiehong Zhao, Miaokun Wang

Published 2023-05-04Version 1

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. Iv\'{a}dy [12, Theorem, (3.2)] in the case of $0<x+y<1$.