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

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

6.

$\Gamma \left(\displaystyle \frac{1}{2}\right) = \sqrt{\pi} = 1.7724\;5385\;0905\;5160\;2729\;8167 \cdots$

7.

$\Gamma \left(\displaystyle \frac{1}{3}\right) = 2.6789\;3853\;4707\;748 \cdots$

[Tables]

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