( ) are the Lagurre polynomials. I would like to derive the following expression:
So far I have shown that the coefficients in any power series solution of will satisfy that:
Furthermore I have shown that
Now, using indcution, I would like to show that:
I have that for . Thus the basis for the induction is established. Now I assume that is true for a fixed and want to derive the case for . I have done the following:
I am stuck here. Suggestions would be greatly appreciated.