E

Redirect to:

• Euler Number

The Euler Number, symbolized e, is a useful mathematical constant which is an irrational 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x}
  
  
• With infinite series - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e=\sum_{n=0}^{\infty}\frac{1}{n!}}