Laguerre–Pólya class

Summary

The Laguerre–Pólya class is the class of entire functions that are limits, uniformly on compact sets, of real polynomials with only real zeros. Its members are described by an explicit Hadamard-type product with real zeros and a Gaussian factor. The class is closed under differentiation, so it is the natural home of real-rootedness for entire functions. It appears in the study of the zeros of the Riemann zeta function and of special functions.