MacLaurin series of Exponential function, ![e^x](../files/exp_ex01_large.png)
The MacLaulin series (Taylor series at ) representation of a function
is
The derivatives of the exponential function and their values at
are:
Note that the derivative of is also
and
. We substitute this value of
in the above MacLaurin series:
We can also get the MacLaurin series of by replacing
to
:
is used in Euler's Equation.