A family of polynomials with concyclic zeros. II
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- by Ronald J. Evans and Kenneth B. Stolarsky PDF
- Proc. Amer. Math. Soc. 92 (1984), 393-396 Request permission
Abstract:
Let ${\lambda _1}, \ldots ,{\lambda _J}$ be nonzero real numbers. Expand \[ E(z) = \prod {( - 1 + \exp {\lambda _j}z)} ,\] 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 $\left | r \right |$ centered at $- r$, where $r = n/\sum {\lambda _j}$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 393-396
- MSC: Primary 30C15; Secondary 33A10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0759660-9
- MathSciNet review: 759660