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Complex Analysis Regarding Essential Singularities

  1. May 25, 2006 #1
    Suppose one has a complex valued function f(z) that possesses an essential singularity at the origin, and at plus and minus 1, and at plus and minus a point "p" of interest on the real number line in the complex plane. Assume that the point is within some length from origin along the real axis less than 10^600. Given a point q on the real number line between 0 and 10^1200, how difficult would it be to determine whether the essential singularity at p is to the right or left of q on the number line? That is, are there any complex analysis techniques that would allow one to discover what direction on the real number line an essential singularity exists in relative to an arbitrary point q on the number line (assuming it is known that an essential singularity exists on the real number line)?


    Edwin G. Schasteen
  2. jcsd
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