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Exponential function

The natural exponential function has as base e and is written as

however only, if x is a natural number.

 


Explanation

Exponential functions play a central role in mathematics. And that is precisely why this constant also is abbreviated with the letter e - of exponent. You can write each number as an exponential function with logarithms as exponent. Trigonometric functions and hyperbolic functions are defined with exponential functions.

 


Power series

The power series for the exponential function can be written as

 


Formulas

Euler's formula shows the connection with hyperbolic functions

Here x is specified in radians.

 


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