natural log base

The natural log base, or $e$ , has value $$ 2.718281828459045\ldots$$

$e$ was extensively studied by Euler in the 1720's, but it was originally discovered by John Napier.

$e$ is defined by $$ \lim_{n \rightarrow \infty} \left(1+\frac{1}{n}\right)^n$$

It is more effectively calculated, however, by using the Taylor series for $f(x)=e^x$ at $x=1$ to get the representation $$ e = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \cdots$$