e

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e is a useful mathematical constant which is a transcendental number approximately equal to 2.718281828459045 . e can be used in logarithms as the base, called a natural logarithm. e is named for Swiss mathematician Leonhard Euler, though he did not discover the constant.

It has some remarkable properties: For example:

\frac{d}{dx}e^x = e^x.

(i.e. the exponetial function is an eigenfunction of the derivative operator, with eigenvalue 1).

Formulae for e

  • With limits - e=\lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x

  • With infinite series - e=\sum_{n=0}^{\infty}\frac{1}{n!}
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