Difference between revisions of "E"
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'''''e''''' is a useful [[mathematical]] constant which is a [[transcendental]] number approximately equal to 2.718281828459045 . ''e'' can be used in [[logarithm]]s as the base, called a [[natural logarithm]]. ''e'' is named for [[Swiss]] mathematician [[Leonhard Euler]], though he did not discover the constant. | '''''e''''' is a useful [[mathematical]] constant which is a [[transcendental]] number approximately equal to 2.718281828459045 . ''e'' can be used in [[logarithm]]s 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 | + | 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> | :<math>\frac{d}{dx}e^x = e^x.</math> | ||
| + | |||
| + | The exponetial function is the [[eigenfunction]] of the derivative operator. | ||
==Formulae for ''e''== | ==Formulae for ''e''== | ||
Revision as of 23:41, June 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.
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>