论文标题
在来自Laguerre-Pólyai类的整个功能上，泰勒系数的第二张商增加了
On the entire functions from the Laguerre-Pólya I class having the increasing second quotients of Taylor coefficients
论文作者
论文摘要
我们证明，如果$ f（x）= \ sum_ {k = 0}^\ infty a_k x^k，$ $ a_k> 0，$是一个完整的函数，使得序列$ q：= \ left（\ frac {a_k^2}非销售和$ \ frac {a_1^2} {a_ {0} a_ {2}} \ geq 2 \ sqrt [3] {2}，$，然后除$ f $的$ f $的所有有限数量都是真实而简单的。我们还以最接近零根的标准为此函数仅具有真实的零（换句话说，是属于laguerre-pólya类型I类）的标准。
We prove that if $f(x) = \sum_{k=0}^\infty a_k x^k,$ $a_k >0, $ is an entire function such that the sequence $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}} \right)_{k=1}^\infty$ is non-decreasing and $\frac{a_1^2}{a_{0}a_{2}} \geq 2\sqrt[3]{2},$ then all but a finite number of zeros of $f$ are real and simple. We also present a criterion in terms of the closest to zero roots for such a function to have only real zeros (in other words, for belonging to the Laguerre--Pólya class of type I) under additional assumption on the sequence $Q.$
