A family of polynomials with concyclic zeros
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- by Kenneth B. Stolarsky
- Proc. Amer. Math. Soc. 88 (1983), 622-624
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702287-4
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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 $r = n/m$.References
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Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 622-624
- MSC: Primary 30C15; Secondary 33A10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702287-4
- MathSciNet review: 702287