Hyperbolicity of Appell polynomials of functions in the $$\delta $$-Laguerre–Pòya class

Abstract

We present a method for proving that Jensen polynomials associated with functions in the $$\delta $$-Laguerre-Polya class have all real roots, and demonstrate how it can be used to construct new functions belonging to the Laguerre–Polya class. As an application, we confirm a conjecture of Ono, which asserts that the Jensen polynomials associated with the first term of the Hardy–Ramanujan–Rademacher series formula for the partition function are always hyperbolic.