E - base of natural logarithm

The constant e (occasionly called Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms) is the base of the natural logarithm. It is approximately equal to

e = 2.71828 18284 59045 23536 02874 .....

It is equal to exp(1) where exp is the exponential function and therefore it is the limit of (1 + 1/n)ⁿ as n goes to infinity and can also be written as the infinite series

e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ...

     _∞ 
 e = ∑ (n!)^-1
    ⁿ⁼⁰

Here n! stands for the factorial of n.

The number e is relevant because one can show that the exponential function exp(x) can be written as e^x; the exponential function is important because it is, up to multiplication by a scalar, the unique function which is its own derivative and is hence commonly used to model growth or decay processes.

The number e is known to be irrational and even transcendental. It features (along with a few other fundamental constants) in the most remarkable formula in the world.

/Talk