English

A lower bound for the beta function

Classical Analysis and ODEs 2023-05-05 v1

Abstract

We present a new lower bound for Euler's beta function, B(x,y)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]×(0,1](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<10<x+y<1.

Keywords

Cite

@article{arxiv.2305.02754,
  title  = {A lower bound for the beta function},
  author = {Tiehong Zhao and Miaokun Wang},
  journal= {arXiv preprint arXiv:2305.02754},
  year   = {2023}
}
R2 v1 2026-06-28T10:25:33.746Z