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Strange behaviour of Plot

  • To: mathgroup at
  • Subject: [mg107588] Strange behaviour of Plot
  • From: "Very Bad Mother..." <shinytinkerbell at>
  • Date: Thu, 18 Feb 2010 05:17:26 -0500 (EST)

I've found it quite puzzling. Pls, have a look.
I define the following functions:

Summand2[j_, m_, \[CapitalDelta]_] :=
  If[j == m, 0,
   2/((j - m)^2 \[CapitalDelta]^2) (-3 +
      Exp[-(((j - m)^2 \[CapitalDelta]^2)/2)] (3 +
         2 (j - m)^2 \[CapitalDelta]^2))];

sigma[m_, Nm_, \[CapitalDelta]_] := NSum[Summand2[j, m, \
[CapitalDelta]], {j, 0, Nm - 1}];

where j and m are supposed to be integers and \[CapitalDelta] to be a
"double" (in C-terms).
Now, I'd like to plot the sigma function:
Plot[sigma[m, 4, 6], {m, 0, 3}]
So, ofcourse, I obtain a plot of a continues function, for all ms
between 0 and 3. From this plot one can find that the values of sigma
for integers are positive and about 0.6. However, what is interesting,
if one evaluates explicitly sigma[m, 4, 6] for m=0, 1, 2, 3, one will
find that actually the values are negative about -0.3.
How is that possible? It's really confusing. Any help appreciated.
Thank you in advance,
Kind regards,

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