# plotting an equation with double summations

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}]

• I and N are built-in symbols, so don't use as custom function or variable names. Please try to come up with a minimal (as short as possible) test case that demonstrates the problem you are having, and describe the problem and the question in detail. If you simply post a large body of code, saying that it doesn't work, but not explaining what you're trying to do and what went wrong, then it's unlikely people will help. Commented Mar 26, 2013 at 16:29
• Thank you Verbeia for the editing!!! Commented Apr 2, 2013 at 12:02

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.

• thank you so much Sjoered C. de Vries. I correcetd my silly mistake and managed to plot the function IIC. Commented Apr 3, 2013 at 8:56
• 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], 100, 0.2]}, {[Nu], 1, 100}], PlotRange -> All, AxesOrigin -> {0, 0}] Commented Apr 3, 2013 at 9:27
• @ Sjoerd C. de Vries-in the expression q[[Nu]_, num_, [CapitalDelta]_, t_] the summations over d & d by 10 simply to see if their is any way to get it to work, if it goes to infinity,that is very slow to complete, is there any way to converge? Commented Apr 5, 2013 at 14:36