Difference between revisions of "E"
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:<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]] operator, with [[eigenvalue]] 1). | + | (i.e. the exponential function is an eigenfunction of the [[Derivative (calculus)|derivative]] operator, with [[eigenvalue]] 1). |
==Formulae for ''e''== | ==Formulae for ''e''== | ||
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>