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Searching list for closest match to p

• To: mathgroup at smc.vnet.net
• Subject: [mg79274] Searching list for closest match to p
• From: chuck009 <dmilioto at comcast.com>
• Date: Mon, 23 Jul 2007 03:41:54 -0400 (EDT)

I'm working on an interesting theorem in Complex Analysis called Jentzsch's Theorem in which the zeros of the partial sums of a Taylor series for an analytic function in the unit disk, all converge to values on the unit disk.  So I choose a point on the unit disk, p=Cos[pi/3]+iSin[pi/3], calculate the normal series for f[x]=Log[1+x] for n ranging from 1 to 100, calculate the zeros, then for each polynomial, search the zeros for the one closest to the point.  Here's my code.  I feel the Table part is messy with the First[First[Position... construct in it.  Can anyone recommend a more concise way of searching the zero lists and finding the one closest to p3?

Thanks,


p3color = Red; 
p3 = Cos[Pi/3] + I*Sin[Pi/3];
 
p3mintable = 
   Table[zlist = x /. N[Solve[Normal[Series[Log[1 + x], {x, 0, nval}]] == 0], 
        6]; minz = zlist[[First[First[Position[mins = (Abs[#1 - p3] & ) /@ 
            zlist, Min[mins]]]]]], {nval, 1, 100}]; 

p3vals = ({Re[#1], Im[#1]} & ) /@ p3mintable; 

lp3 = ListPlot[p3vals, PlotRange -> {{-1.4, 1.4}, {-1.4, 1.4}}, 
    AspectRatio -> 1]; 

Show[{lp3, Graphics[{p3color, PointSize[0.03], Point[{Re[p3], Im[p3]}]}], 
   Graphics[Circle[{0, 0}, 1]]}]

• Follow-Ups:
  • Re: Searching list for closest match to p
    • From: Daniel Lichtblau <danl@wolfram.com>