论文标题
$ \ ell $ -log-Momotonic和Laguerre的不等式
$\ell$-Log-momotonic and Laguerre Inequality of P-recursive Sequences
论文作者
论文摘要
我们考虑$ \ ell $ -log-momotonic序列和laguerre的序列二次序列不等式$ \ {a_n \} _ {n \ ge 0} $，这样，\ [\ frac {a_ {a_ {n-1} a_ {n-1} a_ {n + 1}}}} \ frac {r_i（\ log n）} {n^{n^{α_i}} + o \ left（\ frac {1} {n^β} \ right），$ m $是非听力整数，$α_i$是$ r_i $ $ r_i（$ r_i（$ r_i）， <\ cdots <α_m<β。 \]我们将在$ \ ell $ -LOG-MOMOTONIC序列和Laguerre不等式的$ N $上给出足够的条件。 许多p恢复序列属于此框架。最后，我们将提供一种方法来找到$ n $，以便对于任何$ n \ geq n $，第三顺序的日志摩托车不平等和laguerre的命令不平等。
We consider $\ell$-log-momotonic sequences and Laguerre inequality of order two for sequences $\{a_n\}_{n \ge 0}$ such that \[ \frac{a_{n-1}a_{n+1}}{a_n^2} = 1 + \sum_{i=1}^m \frac{r_i(\log n)}{n^{α_i}} + o\left( \frac{1}{n^β} \right), \] where $m$ is a nonnegative integer, $α_i$ are real numbers, $r_i(x)$ are rational functions of $x$ and \[ 0 < α_1 < α_2 < \cdots < α_m < β. \] We will give a sufficient condition on $\ell$-log-momotonic sequences and Laguerre inequality of order two for $n$ sufficiently large. Many P-recursive sequences fall in this frame. At last, we will give a method to find the $N$ such that for any $n\geq N$, log-momotonic inequality of order three and Laguerre inequality of order two holds.
