Hyperbolicity of Appell Polynomials of Functions in the $��$-Laguerre-P��lya Class

We present a method for proving that Jensen polynomials associated with functions in the $��$-Laguerre-P��lya class have all real roots, and demonstrate how it can be used to construct new functions belonging to the Laguerre-P��lya 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.