On the number of real zeros of entire functions of finite order of grows (Q1711208)

Given an entire function $f$ of the form \[ f(z)=\prod_{k=1}^\infty(1-\frac{z}{\beta_k})=1+\sum_{j=1}^\infty a_jz^j,\quad \beta_k\ne0,\ \beta_k\in \mathbb{R},\ k\in \mathbb{N}, \] the author proves a variant of the Descartes rule of signs that the number of positive zeros of $f$ is equal to the number of sign changes in the sequence of its Taylor coefficients $1,a_1,a_2,\dots$. For the entire collection see [Zbl 1401.30002].