Chapter 7: Power series methods

Many functions can be written in terms of a power series

$$\sum _{k=0}^{\infty} a_k(x-x_0)^k \nonumber$$

If we assume that a solution of a differential equation is written as a power series, then perhaps we can use a method reminiscent of undetermined coefficients. That is, we will try to solve for the numbers $a_k$. Before we can carry out this process, let us review some results and concepts about power series.