Re: Strange behaviour of Plot
- To: mathgroup at smc.vnet.net
- Subject: [mg107592] Re: [mg107588] Strange behaviour of Plot
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Fri, 19 Feb 2010 03:32:37 -0500 (EST)
- Reply-to: hanlonr at cox.net
Your function is discontinuous at integer values of m since you set Summand2 to 0 for j=m. The continuous function that you plotted reflects the limit Limit[2/((j - m)^2 d^2) (-3 + Exp[-(((j - m)^2 d^2)/2)] (3 + 2 (j - m)^2 d^2)), j -> m] 1 So at the integer values of m you are subtracting 1 (using 0 rather than 1 for Summand2[m, m, d] ) and arriving at the negative values. Bob Hanlon ---- "Very Bad Mother..." <shinytinkerbell at googlemail.com> wrote: ============= Hi, 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, tinkerbell