plotting an equation with double summations

Question

Thank you so much for the helpful comments. Now able to manage to plot all the functions.

Remove[q, qC, IIC]

ass = {d > 1, num > 0, \[CapitalDelta] > 0, t > 0, n >= 0};

q[\[Nu]_, num_, \[CapitalDelta]_, t_] := 
 1/num (1 + 
    2 Exp[-\[Nu]] NSum[
      Sin[(\[Pi] d)/num]/((\[Pi] d)/num) Exp[-d \[CapitalDelta]^2] 
       Cos[(\[Pi] d)/num (2 t + 1)] \[Nu]^(n + d/2)/Sqrt[
       n! (n + d)!], {d, 1, 10}, {n, 0, 10}])

AbsoluteTiming[Table[q[2, 4, 0.2, t], {t, 0, 200, 20}]]

Plot[q[2.0, 4.0, 0.2, t], {t, 0, 200}]

qC[\[Nu]_, num_, \[CapitalDelta]_, t_] := 
  1/num (1 + 
     2 Exp[-\[Nu]] Sum[
       Sin[(\[Pi] d)/num]/((\[Pi] d)/num) Exp[-d \[CapitalDelta]^2] 
        Cos[(\[Pi] d)/num (2 t + 1)] \[Nu]^(n + d/2)/Sqrt[
        n! (n + d)!], {d, 1, 20}, {n, 0, 20}]);

AbsoluteTiming[Table[qC[2., 4., 0.2, t], {t, 0, 200, 10}]]

ListPlot[Table[{t, qC[2, 4, 0.2, t]}, {t, 0, 200}]]

IIC[\[Nu]_, num_, \[CapitalDelta]_] := 

Log[2, num] - Sum[(q[[Nu], num, [CapitalDelta], t]) Log[2, q[[Nu], num, [CapitalDelta], t]], {t, 0, num - 1}]; AbsoluteTiming[Table[IIC[[Nu], 4, 0.2], {[Nu], 1, 200, 20}]] ListPlot[Table[{[Nu], IIC[[Nu], 4, 0.2]}, {[Nu], 1, 50}], PlotRange -> All, AxesOrigin -> {0, 0}]

Answer 1

The first plot just works fine, although it takes a long time.

Plot[q[2.0, 4.0, 0.2, t], {t, 0, 200}]

The table contains the same values, because you sample the periodic function periodically.

The data of the second plot is sampled badly. You should increase the frequency:

ListPlot[Table[{t, qC[2, 4, 0.2, t]}, {t, 0, 20, .1}]]

The last plot doesn't work because your function IIC has t both in its argument list as well as in the iterator of the Sum.