E

From specialfunctionswiki
Revision as of 06:48, 4 June 2016 by Tom (talk | contribs)
Jump to: navigation, search

The number $e$ is the number such that $$\displaystyle\int_1^e \dfrac{1}{t} \mathrm{d}t=1.$$ This means, by definition, that $\log(e)=1$, where $\log$ denotes the logarithm.

Properties

Theorem: The folllowing formula holds: $$e=\displaystyle\lim_{k \rightarrow \infty} \left( 1 + \dfrac{1}{k} \right)^k,$$ where $e$ denotes Euler's constant.

Proof:

Theorem: The real number $e$ is irrational.

Proof: proof goes here █

References

Who proved $e$ is irrational?