Chapter 9.2, Problem 72E

Exponential function In Section 9.3, we show that the power series for the exponential function centered at 0 is

$e^x={\displaystyle \underset{k=0}{\overset{\infty }{\sum }}\frac{x^k}{k!},\text{for}-\infty <x<\infty .}$

Use the methods of this section to find the power series for the following functions. Give the interval of convergence for the resulting series.

72. f(x) = x²e^x