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Re: graphing x^2 + 4 on x, y, nad i

  • To: mathgroup at
  • Subject: [mg61890] Re: graphing x^2 + 4 on x, y, nad i
  • From: Scott Hemphill <hemphill at>
  • Date: Thu, 3 Nov 2005 04:59:08 -0500 (EST)
  • References: <dka06q$6v1$>
  • Reply-to: hemphill at
  • Sender: owner-wri-mathgroup at

"G. Raymond Brown" <gbrown at> writes:

> Thanks.  This provides an illuminating depiction of complex functions at
> both zeros and poles.

Another thing it can do is to depict the radius of convergence of a Taylor

For example: 1/(1-z) = 1 + z + z^2 + ...

Plot4D[f_, args___] := Plot3D[{Abs[f], Hue[arg[f]/(2*Pi)]}, args]
arg[z_] := Arg[z]
arg[0. + 0.I] = 0  (* Arg[0.+0.I] is undefined; fix it *)

p[n_] := Plot4D[Sum[z^k,{k,0,n}], {x,-1,1}, {y,-1,1}, PlotRange->{0,20}]

The radius of convergence is one, which is clearly visible in the plot:


You can get Mathematica to plot 1/(1-z) by executing:


The sum doesn't actually converge outside the radius of convergence,
but Mathematica conveniently(?) ignores that fact.

Scott Hemphill	hemphill at
"This isn't flying.  This is falling, with style."  -- Buzz Lightyear

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