e

The symbol e is used almost exclusively to represent the Euler number (aka Euler constant), who value is approximately 2.71828. It may be defined as the limit

\[\lim_{n\rightarrow\infty} \left( 1+ \frac{1}{n}\right) \]

or as the series

\[\sum_{n=0}^{\infty} \frac{1}{n!} = 1 + \frac{1}{2} + \frac{1}{6}+\frac{1}{24}+\cdots\]

Both the logarithm with base e (the so-called natural logarithm) and the exponential function with base e (i.e., the function \(f(x)=e^x\)) are of central importance in many fields of pure and applied mathematics.