Is there a way to automatically Collect[] the ω terms by their powers for this expression?
expression=Sum[I*E^(I*m*t*ω)*m*ω*p[1, m, t] + E^(I*m*t*ω)*Derivative[0, 0, 1][p][1, m, t], {m, 1, mlimit}]/ω;
Collect[ExpandAll[expression], ω]
This just returns expression
-- it fails to separate terms within the summations. What I really want is this:
Sum[I*E^(I*m*t*ω)*m*p[1, m, t], {m, 1, mlimit}] + Sum[E^(I*m*t*ω)*Derivative[0, 0, 1][p][1, m, t], {m, 1, mlimit}]/ω