Is it this what you want?
p1 = Plot[1/m - m/2 - Cot[m], {m, 1, 30}]
here you can (by GetCoordinates) get some approximate values of zeroes
prox = {{5.692,
0.1677}, {8.554, -2.711}, {12.01, -4.356}, {14.62, -6.207}, \
{17.98, -8.057}, {21.18, -9.496}, {24.21, -11.14}, {27.5, -12.79}}
Use this to find the (approx) zeros
prox1 = Transpose[prox][[1]]
zeros = FindRoot[1/m - m/2 - Cot[m] == 0, {m, #}] & /@ prox1
Then
zeros1 = zeros /. {m -> x_} -> x
u=x Exp[-#] & /@ zeros1
u1=u // Total