$$\small{\text{$
2.5! = \Gamma{(2.5+1)}
$
}}$$
$$\small{ \text{ Formula }
\boxed{
\begin{array}{lcl}
\Gamma{(x+1)} = x\cdot\Gamma{(x)} \\
\Gamma{(\frac12)} = \sqrt{\pi}
\end{array}
}
}$$
$$\small{
\begin{array}{lcl}
2.5!&=& \Gamma{(2.5+1)}\\
&=& 2.5\cdot\Gamma{(2.5)}\\
&=& 2.5\cdot \Gamma{(1.5+1)}\\
&=& 2.5\cdot 1.5\cdot \Gamma{(1.5)}\\
&=& 2.5\cdot 1.5\cdot \Gamma{(\frac12+1)}\\\\
&=& 2.5\cdot 1.5\cdot \frac12 \cdot \Gamma{(\frac12)}\\\\
&=& 2.5\cdot 1.5\cdot \frac12 \cdot \sqrt{\pi}\\\\
&=& 1.875 \cdot \sqrt{\pi} \\
&\approx& 1.875 \cdot 1.77245385091 \\
\mathbf{2.5!} &\mathbf{\approx}& \mathbf{3.32335097045}
\end{array}
}$$
.
Thanks for letting us know,
Yes Wolfram|Alpha agrees with your figure of 3.32335... (maybe that is where you got?)
http://www.wolframalpha.com/input/?i=2.5%21
web2.0 calc
$${\mathtt{2.5}}{!} = {\mathtt{3.320\: \!382\: \!507\: \!505\: \!424}}$$
I don't know where else to look it up.
It is most likely a rounding error.
I will leave a note for admin.
$$\small{\text{$
2.5! = \Gamma{(2.5+1)}
$
}}$$
$$\small{ \text{ Formula }
\boxed{
\begin{array}{lcl}
\Gamma{(x+1)} = x\cdot\Gamma{(x)} \\
\Gamma{(\frac12)} = \sqrt{\pi}
\end{array}
}
}$$
$$\small{
\begin{array}{lcl}
2.5!&=& \Gamma{(2.5+1)}\\
&=& 2.5\cdot\Gamma{(2.5)}\\
&=& 2.5\cdot \Gamma{(1.5+1)}\\
&=& 2.5\cdot 1.5\cdot \Gamma{(1.5)}\\
&=& 2.5\cdot 1.5\cdot \Gamma{(\frac12+1)}\\\\
&=& 2.5\cdot 1.5\cdot \frac12 \cdot \Gamma{(\frac12)}\\\\
&=& 2.5\cdot 1.5\cdot \frac12 \cdot \sqrt{\pi}\\\\
&=& 1.875 \cdot \sqrt{\pi} \\
&\approx& 1.875 \cdot 1.77245385091 \\
\mathbf{2.5!} &\mathbf{\approx}& \mathbf{3.32335097045}
\end{array}
}$$