Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A family of polynomials with concyclic zeros

Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 88 (1983), 622-624
MSC: Primary 30C15; Secondary 33A10
MathSciNet review: 702287
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Abstract: Expand $ E\left( z \right) = {({e^z} - 1)^m}$ by the binomial theorem, and replace every $ exp\left( {{k_z}} \right)$ by its approximation $ {\left( {1 + k{n^{ - 1}}z} \right)^n}$. The resulting polynomial has all of its zeros on a circle of radius $ r$ centered at $ - r$, where $ r = n/m$.

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Keywords: Concyclic zeros, exponential, exponential polynomial, linear fractional transformation, "reductionism", zeros of polynomials
Article copyright: © Copyright 1983 American Mathematical Society