Difference between revisions of "E"
From specialfunctionswiki
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=References= | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm at -i|next=e is limit of (1+1/n)^n}}: 4.1.16 | ||
[http://eulerarchive.maa.org/hedi/HEDI-2006-02.pdf Who proved $e$ is irrational?] | [http://eulerarchive.maa.org/hedi/HEDI-2006-02.pdf Who proved $e$ is irrational?] | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 06:46, 4 June 2016
The number $e$ can be defined in the following way: let $f$ be the unique solution of the initial value problem $$y'=y;y(0)=1,$$ then $e=f(1)$.
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
