Difference between revisions of "E"
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The exponetial function is the [[eigenfunction]] of the derivative operator. | The exponetial function is the [[eigenfunction]] of the derivative operator. | ||
| − | == | + | ==Calculations for ''e''== |
*With limits - <math>e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x</math><br /><br /> | *With limits - <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 17:18, July 2, 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 that its exponential to any real number <math>x</math> is:
- <math>\frac{d}{dx}e^x = e^x.</math>
The exponetial function is the eigenfunction of the derivative operator.
Calculations 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>