Difference between revisions of "E"
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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 | + | * {{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 17:27, 27 June 2016
We define the real number $e$ to be the number such that $$\displaystyle\int_1^e \dfrac{1}{t} \mathrm{d}t=1.$$ By the definition of the logarithm, we have $\log(e)=1$. The value of $e$ is $$e=2.71828182846\ldots.$$
Properties
Euler's formula
e is irrational
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.16$
