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expression=Sum[I*E^(I*m*t*[Omega])*m*[Omega]*p[1, m, t] + E^(I*m*t*[Omega])*Derivative[0, 0, 1][p][1, m, t], {m, 1, mlimit}]/[Omega];
Collect[ExpandAll[expression], [Omega]]
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