# e (mathematics)

It has been suggested that this article or section be merged with natural logarithm. (Discuss)
It has been suggested that this article or section be merged with e. (Discuss)

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, the slope of the exponential curve is the same as its value:

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

(i.e. the exponential 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 - $e=\sum_{n=0}^{\infty}\frac{1}{n!}$