Can you upload a worksheet with attempted solution? 

To @acer and @mmcdara

I am sorry for my very late response. I posted this question and then I had to step away from the problem for a while and now I am back into it. 

Thank you both for the replies, I was unaware that I could get it to run that quickly, must not have been thinking hard enough. Both of your responses make sense, but if something else comes up I will be sure to ask. 

Thank you again. 

@Scot Gould 

..

@dharr 

Thank you. Yes something like that but I don't think it fully solves my problem. I will reformulate. 

However, you are correct E2 is a mess, and that is a construct of how I want to solve the problem. I can elaborate in more detail and that might make it more clear what I was hoping for, I will edit my question afterwords. The differential equation I want to solve is: 

Sum((-1)^n*n*2^(n - 1)*a[n]*diff(Phi(r), r)^(-1 + 2*n), n = 1 .. N)=Q/r

I want the solution for Phi(r) to be of the form

diff(Phi(r), r) = Sum(b[i]/r^i, i = 1 .. infinity)

Now say I truncate the first sum to N=2 and I want to get the first few coefficients b[i] which solve this equation, obviously this is an infinite sum but if we consider just the first few terms for simplicity

We have that b[1]=-Q,b[2]=0,b[3]=4a[2]Q^3 so on and so on. Is there a command that can do this while considering what the previous found coefficients are (ie set b[1]=Q,b[2]=0)? 

For some reason it doesn't like using f[4](0). If you change to f[4] it works fine for me. 

@Paras31 

I will continue to look at this. 

@Paras31 

I can plot yes. If those are the plots you are looking for let me dive a little deeper into it and get back to you ASAP. 

@Paras31

Try this one:

dsolve_fix_2.mw

You don't have a differential equation that is why you are getting the error. This is a integral equation, you would want to use the intsolve command. Although in doing this I do not get a solution. 

It is possible the plots created do not match the numeric values they state. My results match yours and do not match theirs even for the gamma=0.1 case, I only get the gamma=0.1 behaviour they show if my value is around 0.2. 

I got no errors, answer returned

Dsolve_Reply.mw

@ecterrab 

Thank you as well. 

@C_R 

I assumed that it was something like this, good to know my suspicions were correct. 

You are using multiplications between your partials and your potentials, you need to use d_[mu](A) if you want to have the partial actually evaluate on A. Secondly,  in other spots you are not multiplying two terms together just writing a single term (example gr, should be g*r). 

I think I fixed your problems in the attached code. Also, shouldnt you have some of your indices in a one up one down configuation in F? 

SU(2)_Reply.mw

@segfault 

Good luck with whatever you are trying to accomplish.