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