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We present a method for proving that Jensen polynomials associated withfunctions in the $\delta$-Laguerre-P\'olya class have all real roots, anddemonstrate how it can be used to construct new functions belonging to theLaguerre-P\'olya class. As an application, we confirm a conjecture of Ono,which asserts that the Jensen polynomials associated with the first term of theHardy-Ramanujan-Rademacher series formula for the partition function are alwayshyperbolic.

Hyperbolicity of Appell Polynomials of Functions in the $\delta$-Laguerre-P\'olya Class