m0[e_]:=Power[2,-e] + 3 Power[3,-e/2] + 6 Power[2,-e/2]

t0[e_]:=6 Power[3,e/2]/Power[8,e/2]

cutoff =1;
m1[e_]:=t0[e]+3 Power[2,-e] + Power[cutoff,-e]-m0[e]
n1[e_]:=t0[e]+2 Power[2,-e] + 2            -m0[e]