This is an old revision of this page, as edited by Rgamble (talk | contribs) at 10:19, 30 March 2002 (Reverting from 62.98.136.xxx 's extension of the constant e to 20 or so lines. I say it's vandalism.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
Revision as of 10:19, 30 March 2002 by Rgamble (talk | contribs) (Reverting from 62.98.136.xxx 's extension of the constant e to 20 or so lines. I say it's vandalism.)(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)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) 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!)
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; 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.