论文标题
Hutchinson的间隔和Laguerre-Pólya课程的全部功能
Hutchinson's intervals and entire functions from the Laguerre-Pólya class
论文作者
论文摘要
我们找到间隔的$ [α，β（α）$，以便如果单变量实际多项式或整个函数$ f（z）= a_0 + a_1 z + a_1 z + a_2 z^2 + \ cdots $，具有正系数满足条件$ \ frac {a___ {a_ {a_ {a_ {k-1}^2}^2} a____________ {所有$ k \ geq 2，然后$ f $属于laguerre--pólya类的β（α）] $。例如，从J.I.〜Hutchinson的定理中，可以观察到$ f $属于Laguerre-pólya类（仅具有真正的零）时，当$ q_k（f）\ in [4， + \ infty）中。$，我们有兴趣找到那些不是$ [4， + \ f infty的subsets的间隔。
We find the intervals $[α, β(α)]$ such that if a univariate real polynomial or entire function $f(z) = a_0 + a_1 z + a_2 z^2 + \cdots $ with positive coefficients satisfy the conditions $ \frac{a_{k-1}^2}{a_{k-2}a_{k}} \in [α, β(α)]$ for all $k \geq 2,$ then $f$ belongs to the Laguerre--Pólya class. For instance, from J.I.~Hutchinson's theorem, one can observe that $f$ belongs to the Laguerre--Pólya class (has only real zeros) when $q_k(f) \in [4, + \infty).$ We are interested in finding those intervals which are not subsets of $[4, + \infty).$
