Monday, February 1, 2010

MacLaurin series of Exponential function,

The MacLaulin series (Taylor series at

) representation of a function

The derivatives of the exponential function

and their values at

are:

Note that the derivative of

is also

and

. We substitute this value of $f^{(n)}(0)$ in the above MacLaurin series:
MacLaurin series of e^x

We can also get the MacLaurin series of $e^{ix}$ by replacing

:
$MacLaurin series of e^{ix}$