e

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>