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:

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

(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 - $e=\sum _{n=0}^{\infty }{\frac {1}{n!}}$