论文标题
在最接近零根和第二个泰勒系数的泰勒系数的第二次。
On the closest to zero roots and the second quotients of Taylor coefficients of entire functions from the Laguerre-Pólya I class
论文作者
论文摘要
对于整个函数，$ f（z）= \ sum_ {k = 0}^\ infty a_k z^k，a_k> 0，$，我们表明，如果$ f $属于laguerrerea-pólya类，$ q_k：q_k：q_k：= \ frac {a____ {a__ {a_ {a_ {k-1}^2}^2}^2}^2}满足条件$ q_2 \ leq q_3，$ then $ f $在细分市场中至少有一个零，$ [ - \ frac {a_1} {a_2} {a_2}，0]。$我们还提供了必要的条件和足够的条件，并有足够的条件，并且在$ q_k $ $ k = 2,3,3，4。$ q_k $中的这种情况下存在这样的零条件。
For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k, a_k>0,$ we show that if $f$ belongs to the Laguerre-Pólya class, and the quotients $q_k := \frac{a_{k-1}^2}{a_{k-2}a_k}, k=2, 3, \ldots $ satisfy the condition $q_2 \leq q_3,$ then $f$ has at least one zero in the segment $[-\frac{a_1}{a_2},0].$ We also give necessary conditions and sufficient conditions of the existence of such a zero in terms of the quotients $q_k$ for $k=2,3, 4.$
