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Re: Corrupt graphics output

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90697] Re: Corrupt graphics output
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sat, 19 Jul 2008 04:52:08 -0400 (EDT)
  • References: <g5pj0s$qbg$1@smc.vnet.net>

If you are using Version 6 you don't need a lot of PlotPoints. You can 
control things better using MaxRecursion. The following gives a fairly 
decent representation:

Plot3D[Abs[Gamma[x + I y]], {x, -5.5, 5}, {y, -2, 2},
 PlotPoints -> {20, 5},
 MaxRecursion -> 4,
 PlotRange -> {0, 10},
 BoxRatios -> {10.5, 4, 8},
 AxesLabel -> {Re[z], Im[z], Abs[Gamma[z]]}]

Each of the poles should have infinite height but instead they have smaller 
height for the more negative poles. One method to supplement the graphic is 
to add a table of the residues obtained by integrating around each pole.

poles = {0, -1, -2, -3, -4, -5};
Table[{z0,
   With[{\[CapitalDelta] = .05},
    NIntegrate[
      Gamma[z], {z, z0 - \[CapitalDelta] - I \[CapitalDelta],
       z0 + \[CapitalDelta] - I \[CapitalDelta],
       z0 + \[CapitalDelta] + I \[CapitalDelta],
       z0 - \[CapitalDelta] + I \[CapitalDelta],
       z0 - \[CapitalDelta] - I \[CapitalDelta]}] // Abs]}, {z0,
   poles}] // TableForm

0   6.28319
-1  6.28319
-2  3.14159
-3  1.0472
-4  0.261799
-5  0.0523599

-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"Paul M" <paul at somewhere.com> wrote in message 
news:g5pj0s$qbg$1 at smc.vnet.net...
> Hello,
>
> I was playing around with Mathematica the other day and was attempting
> to graph the modulus of the complex-valued gamma function.  When I use
> a PlotPoints value of 120 the graph looks fine.  However, the
> following command yields a corrupt graph (PlotPoints value of 150).
>
> Plot3D[Abs[Gamma[x + I y]], {x, -5, 5}, {y, -5, 5},
> PlotPoints -> {150, 150}, PlotRange -> {0, 10},
> BoxRatios -> {1, 1, 0.8}, AxesLabel -> {x, I y, Abs[Gamma[z]]}]
>
> Anyone know the reason for this and possible solutions?
>
> Thank you,
> Paul
> 



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