# e

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. For example:

$\frac{d}{dx}e^x = e^x.$

(i.e. the exponetial function is an eigenfunction of the derivative operator, with eigenvalue 1).

## Formulae for e

• With limits - $e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x$

• With infinite series - $e=\sum_{n=0}^{\infty}\frac{1}{n!}$