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Re: graphing x^2 + 4 on x, y, nad i
*To*: mathgroup at smc.vnet.net
*Subject*: [mg61890] Re: graphing x^2 + 4 on x, y, nad i
*From*: Scott Hemphill <hemphill at hemphills.net>
*Date*: Thu, 3 Nov 2005 04:59:08 -0500 (EST)
*References*: <dka06q$6v1$1@smc.vnet.net>
*Reply-to*: hemphill at alumni.caltech.edu
*Sender*: owner-wri-mathgroup at wolfram.com
"G. Raymond Brown" <gbrown at runbox.com> 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
series.
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 *)
z=x+I*y
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:
p[100]
You can get Mathematica to plot 1/(1-z) by executing:
p[Infinity]
The sum doesn't actually converge outside the radius of convergence,
but Mathematica conveniently(?) ignores that fact.
Scott
--
Scott Hemphill hemphill at alumni.caltech.edu
"This isn't flying. This is falling, with style." -- Buzz Lightyear
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