Talk:Gautschi's inequality

Flipped inequalities?

The inequalities in the last line of the article:

For $s\in (0,1)$, this leads to:

${\frac {(x+1)^{x+1}}{(x+s)^{x+s}}}e^{s-1}<{\frac {\Gamma (x+1)}{\Gamma (x+s)}}<{\frac {(x+1/2)^{x+1/2}}{(x+s-1/2)^{x+s-1/2}}}e^{s-1}.$

Appear to be flipped (the upper bound is the lower bound, etc). Is the original article cited for this bound correct? Topoltergeist (talk) 16:26, 6 December 2024 (UTC)