The point is a regular singular point.

Therefore, solutions shall have the form .

The equation associated with finding is: .

First we do the case when .

We looking for a solution .

Substituting that into the equation we get,

This becomes,

We can rewrite this as,

Evaluate the middle summation at and combine,

This tells us that .

The condition in the middle says,

Thus,

As a consequence

Taking to be arbitrary (like ) shall produce coefficients for .

That would be one solution to the differencial equation.

Of course the other linearly independent solution is found with .