Some Important Constants

1.
$\pi = 3.1415\;9265\;3589\;7932\;3846\;2643\; \cdots$
2.
$\mbox{e} = 2.7182\;8182\;8459\;0452\;3536\;0287 \cdots= \lim_{n \rightarrow \infty}\left(1 + \displaystyle \frac{1}{n}\right)^n$
3.
$\mbox{e}^{\displaystyle\pi} = 23.1406\;9263\;2779\;2690\;06 \cdots$
4.
$\pi^{\displaystyle\mbox{e}} = 22.4591\;5771\;8361\;0454\;7342\;715 \cdots$
5.
Euler's constant

\begin{displaymath}\begin{array}{lcl}
\gamma &=& 0.5772\;1566\;4901\;5328\;6060\...
... \cdots + \displaystyle \frac{1}{n} - \ln(n)\right)
\end{array}\end{displaymath}

6.
$\Gamma \left(\displaystyle \frac{1}{2}\right) = \sqrt{\pi} = 1.7724\;5385\;0905\;5160\;2729\;8167 \cdots$
7.
$\Gamma \left(\displaystyle \frac{1}{3}\right) = 2.6789\;3853\;4707\;748 \cdots$

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