Exponential function In Section 9.3, we show that the power series for the exponential function centered at 0 is
Use the methods of this section to find the power series for the following functions. Give the interval of convergence for the resulting series.
f(x) = x2ex
We are given that for
We have to find the power series for
It is a fact that the x’s outside the series is not going to affect the interval of convergence.
The radius of convergence in the resulting series is
Therefore the interval of convergence is
The power series representation is