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## Homework Statement

[itex]

\begin{equation}

1 - x + \frac{x^2}{(2!)^2} - \frac{x^3}{(3!)^2} + \frac{x^4}{(4!)^2} +.... = 0 \nonumber

\end{equation}

[/itex]

## Homework Equations

To find out the power series in the LHS of the given equation.

## The Attempt at a Solution

I have tried to solve it by constructing a differential equation for the LHS expression (=g(x) say) as:

[itex]

\begin{equation}

(xg(x)')' + g(x) =0 \nonumber

\end{equation}

[/itex]

which gives the solution for g(x) as Bessel function of first kind and zero order.

But, I am still not fully convinced regarding the idea of "recognising" the power series in the LHS. Is there any other algebraic approach towards this problem ?