Number e
The number e is a transcendental number with the value
It is an important number because it forms the connection between powers, logarithms and trigonometric functions.
Power series
The power series for the number e can be written as
or if you prefer
Exponential functions
The number e is the basis of the exponential function
where x is a variable.
Base of the natural logarithm
You can write every number as an exponential function
Because bx conforms to the rules for logarithms as exponents, it applies
for every real number x.
Own derivative
The derivative of the exponential function is
and therefor the exponential function is its own derivative!
Eulers formula
The formula of Euler shows the relation between complex exponential functions and trigonometric functions, as in
Hyperbolic functions
All trigonometric and hyperbolic functions are defined by exponential functions, as for the hyperbolic sine
HistoryThe letter e stands for exponent, but everyone calls it the e from Euler, after the famous Swiss mathematician Leonhard Euler (1707 - 1783) who explained its great significance. |