$δ$ -Laguerre-Pólya类函数的Appell多项式的双曲性
Hyperbolicity of Appell Polynomials of Functions in the $δ$-Laguerre-Pólya Class
摘要：
我们提出了一种方法来证明与$δ$ -Laguerre-Pólya类中的函数相关联的Jensen多项式具有所有的实根，并演示了如何使用它来构造属于Laguerre-Pólya类的新函数。作为应用，我们证实了小野的一个猜想，该猜想断言与分拆函数的Hardy-Ramanujan-Rademacher级数公式的首项相关的Jensen多项式总是双曲的。
英文摘要：
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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