E
From specialfunctionswiki
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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.16