On the zero attractor of the Euler polynomials

  • Boyer R
  • Goh W
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Abstract

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szegö curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed. © 2006.

Author-supplied keywords

  • Argument principle
  • Bernoulli polynomials
  • Euler polynomials
  • Jensen's inequality
  • Saddle point method

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Authors

  • Robert Boyer

  • W. M Y Goh

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