On the zero attractor of the Euler polynomials

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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.




Boyer, R., & Goh, W. M. Y. (2007). On the zero attractor of the Euler polynomials. Advances in Applied Mathematics, 38(1), 97–132. https://doi.org/10.1016/j.aam.2005.05.008

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