May I confirm if my approach is correct so far as I work towards the solution.
I apologize in advance, it looks a bit long, but it is just the first few steps of the approach (no work on equating coefficients etc yet)
1) This ODE has a regular singular point at x=0 and so Frobenius Method is used where
2) If 1) is correct, when I try to write it out as a series I obtain 3 series:
Which simplifies to:
May I confirm if this is correct?
3) My next question is that I attempt to make the summation indexes the same - i.e. n=5. However I get a large number of terms that need to be taken out of the first 2 series - so wanted to confirm if my approach is correct in the first place.
Thank you for any feedback given