 Such entire functions form the Laguerre–Pólya class, which can also be characterized in terms of the Hadamard product, namely, "f" belongs to this class if and only if in the Hadamard representation all "zn" are real, "p" ≤ 1, and "P"("z") = "a" + "bz" + "cz"2, where "b" and "c" are real, and "c" ≤ 0.For example, the sequence of polynomials 

converges, as "n" increases, to exp(−("z"−"d")2).The polynomials 

have all real roots, and converge to cos("z").