A family of polynomials with concyclic zeros. II

Ronald J. Evans, Kenneth B. Stolarsky
1984 Proceedings of the American Mathematical Society  
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
more » ... r C to the polynomials over C that replaces exp(az) by
doi:10.1090/s0002-9939-1984-0759660-9 fatcat:6p3e32wn7zf2rjyqz2xfz77bze