Difference between revisions of "E"
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| − | ''''' | + | The '''Euler Number''', symbolized ''e'', is an irrational [[transcendental]] number approximately equal to 2.718281828459045 . It can be used in [[logarithm]]s 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 | + | It has some remarkable properties. For example: |
:<math>\frac{d}{dx}e^x = e^x.</math> | :<math>\frac{d}{dx}e^x = e^x.</math> | ||
| − | [[ | + | (i.e. the exponential function is an eigenfunction of the [[Derivative (calculus)|derivative]] operator, with [[eigenvalue]] 1). |
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| + | ==Formulae for ''e''== | ||
| + | *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> | ||
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| + | [[Category:Mathematics]] | ||
Latest revision as of 21:18, September 8, 2020
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>