A lower bound for the beta function
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....
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| creator | Zhao, Tiehong Wang, Miaokun |
| description | 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 |
| doi_str_mv | 10.48550/arxiv.2305.02754 |
| format | Article |
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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
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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
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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 $0<x+y<1$.</abstract><doi>10.48550/arxiv.2305.02754</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Classical Analysis and ODEs |
| title | A lower bound for the beta function |
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