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