I am having a little trouble finding the two linearly independent Frobenius solutions of the following differential equation:
I have got as far as finding out the recurrence relations:
note ak is a with subscript k and a(k-1) is a with subscript (k-1)
In the solutions I have it says the above equation and then hence:
where a0 is a with subscript 0
The solutions again have the above line and hence:
However I really do not know how in the solutions they have got from each ak equation to the hence part.
Any help appreciated.