Here's the problem. Equation
needs to be solved using Frobenius method at .
First, I've translated the origin, , so that the original equation becomes
derivatives staying the same,
Now, we seek solution in the form
Upon differentiating and substituting, we get
I hope I've done everything right by now. Now, I'm not sure if my indicial equation is right. First, I shifted the second sum so it becomes
I've taken to be indicial eqation and then plugged the solutions ( and ). Recurrence formula for gives trivial solution and formula for gives polynomial solution.
But, if I use
as a solution, I get in the polynomial and it diverges for . However, if I start the sum with index 1, the solution seems right.
So, I'm just wondering if I did everyting right, especially with indicial equation.
Thanks in advance!