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A family of polynomials with concyclic zeros. II

1984
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Proceedings of the American Mathematical Society
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Let Ai,..., Aj be nonzero real numbers. Expand E(z) = Yl(-l + expX3z), rewrite products of exponentials as single exponentials, and replace every exp(az) by its approximation (1 + an~lz)n, where n > J. The resulting polynomial has all zeros on the (possibly infinite) circle of radius \r\ centered at -r, where r = n/YL^j-1. Introduction. Our purpose is to establish Conjecture [1] of [S2]. For positive integers n let Pn be the linear mapping from the exponential polynomials over C to the polynomials over C that replaces exp(az) by

doi:10.1090/s0002-9939-1984-0759660-9
fatcat:6p3e32wn7zf2rjyqz2xfz77bze