Difference between revisions of "E"
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==Formulae for ''e''== | ==Formulae for ''e''== | ||
| − | *With | + | *With [[limit]]s - <math>e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x</math><br /><br /> |
| − | *With infinite series - <math>e=\sum_{n=0}^{\infty}\frac{1}{n!}</math> | + | *With [[infinite series]] - <math>e=\sum_{n=0}^{\infty}\frac{1}{n!}</math> |
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 16:16, November 3, 2008
e is a useful mathematical constant which is a transcendental number approximately equal to 2.718281828459045 . e can be used in logarithms as the base, called a natural logarithm. e is named for Swiss mathematician Leonhard Euler, though he did not discover the constant.
It has some remarkable properties: For example:
- <math>\frac{d}{dx}e^x = e^x.</math>
(i.e. the exponetial function is an eigenfunction of the derivative operator, with eigenvalue 1).
Formulae for e
- With limits - <math>e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x</math>
- With infinite series - <math>e=\sum_{n=0}^{\infty}\frac{1}{n!}</math>