Hyperbolicity of Appell Polynomials of Functions in the $δ$-Laguerre-Pólya Class

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

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