# 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}]

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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. – Szabolcs Mar 26 '13 at 16:29
Thank you Verbeia for the editing!!! – David H Apr 2 '13 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.

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thank you so much Sjoered C. de Vries. I correcetd my silly mistake and managed to plot the function IIC. – David H Apr 3 '13 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}] – David H Apr 3 '13 at 9:27
@herman If you like the answer, please upvote and/or accept it (using the check mark button). – Sjoerd C. de Vries Apr 3 '13 at 13:59
@ 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? – David H Apr 5 '13 at 14:36