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arXiv · 2305.02754

A lower bound for the beta function

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

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Tiehong Zhao, Miaokun Wang. 2023-05-04. A lower bound for the beta function. https://arxiv.org/abs/2305.02754

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