Assume that can be expressed as a polynomial.

Therefore

.

To find , let .

So .

To find , take the derivative of both sides, then set .

So

To find , take the derivative of both sides, then set .

So

.

To find , take the derivative of both sides, then set

So

.

I think it's relatively easy to see that all the coefficients will be equal to 1.

So .

We can also realise this using the fact that for a convergent infinite geometric series

provided .

If we take and , we find

, provided that .