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A family of polynomials with concyclic zeros. II

Authors: Ronald J. Evans and Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 92 (1984), 393-396
MSC: Primary 30C15; Secondary 33A10
MathSciNet review: 759660
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\lambda _1}, \ldots ,{\lambda _J}$ be nonzero real numbers. Expand

$\displaystyle E(z) = \prod {( - 1 + \exp {\lambda _j}z)} ,$

rewrite products of exponentials as single exponentials, and replace every $ \exp (az)$ by its approximation $ {(1 + a{n^{ - 1}}z)^n}$, where $ n \geqslant J$. The resulting polynomial has all zeros on the (possibly infinite) circle of radius $ \left\vert r \right\vert$ centered at $ - r$, where $ r = n/\sum {\lambda _j}$.

References [Enhancements On Off] (What's this?)

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Keywords: Concyclic zeros, exponential, exponential polynomial, linear fractional transformations, zeros of polynomials
Article copyright: © Copyright 1984 American Mathematical Society

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