partial answer

Joe Riel — Sat, 14 Jan 2012 02:06:49 Z

Rather than starting a new thread it is generally better to continue the old. Regardless, a few comments.

My suggestion to use ?add instead of ?sum was incomplete. The forward quotes which you used are not needed and not appropriate when using add. A more serious problem is that you are using the name of the procedure (f), in the procedure. While Maple can recurse, the recursion must eventually halt, and there is nothing in the procedure that does that. The real problem is that you want f[1] to be a different procedure than f. Alas, Maple treats them as the same. For example

f := x -> f[1](x):
f(3);
Error, (in f[1]) too many levels in recursion

It isn't clear why you are calling f[1](x). Is that supposed to be a completely inert call. In that case, you would be better naming it as f1. That is, you could do

N := 2:
f := eta -> add(cat('f',i)(eta)*m^i, i=0..N):
f(3);
                                                       2
                              f0(3) + f1(3) m + f2(3) m

MaplePrimes - answers and comments on Question, Collecting coefficient of perturbation equations

partial answer