Difference between revisions of "E"
From specialfunctionswiki
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$$e=2.71828182846\ldots.$$ | $$e=2.71828182846\ldots.$$ | ||
=Properties= | =Properties= | ||
| + | [[Euler's formula]]<br /> | ||
<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
<strong>Theorem:</strong> The folllowing formula holds: | <strong>Theorem:</strong> The folllowing formula holds: | ||
Revision as of 04:07, 7 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
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
