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The constant e (occasionally 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) 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! + ...

Here n! stands for the factorial of n.

The infinite continued fraction expansion of e contains an interesting pattern as follows:

e = .

The number e is relevant because one can show that the exponential function exp(x) can be written as e; 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.