A Generalization of the Laguerre–Pólya Class of Entire Functions Original Research Article

Let Θ be a set of real numbers unbounded on both sides and let B be a finite set of positive integers. We characterize the entire functions that can be uniformly approximated on bounded sets by polynomials of the form ∏j∈B pj(zj), where each pj(z) is a polynomial with zeros in Θ.