Difference between revisions of "E"
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==Formulae for ''e''== | ==Formulae for ''e''== | ||
| − | *With [[limit]]s - <math>e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x</math> | + | *With [[limit]]s - <math>e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x</math> |
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*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]] |
Revision as of 11:50, July 13, 2016
The Euler Number, symbolized e, is an irrational transcendental number approximately equal to 2.718281828459045 . It can be used in logarithms as the base, called a natural logarithm. It 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 exponential 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>