论文标题
在某些结果的Schur类型公式
On some resultants formulas of Schur type
论文作者
论文摘要
令$（r_ {a，n}（x））_ {n \ in \ mathbb {n}} $是一系列多项式的序列，带有来自字段$ k $的系数，使重复关系$ r_ {a，n}（a，n}（a，n}（x）（x）= \ sum_ = \ sum_ {|α{|α| \ leq m m} t_{α,n}(x)\textbf{r}_{A,n}^α(x)$ of order $d+1 \in \mathbb{N}_{+}$, where $t_{α,n} \in K[x]$, $m \in \mathbb{N}_{+}$ are fixed, $α\ in \ mathbb {n}^{d+1} $，$ |α| =α_0 + \ \ ldots +α_d$和$ \ textbf {r} _ {a，n}^α（x）= r_ {a，n-1}^{α_0}（x）r_ {x）r_ {a，n-2}^{a，n-2}^{α_1}（x）我们表明，在对初始多项式的轻度假设下，$ r_ {a，0}，\ ldots，r_ {a，d} $和系数$ t_ {α，n} $，我们可以为结果$ \ text {res}（r_ n} r_ {a，n}，r_ r_ {a，n-1-1}提供结果$ \ text {res} {res} {res}（r_ sexterals $ \ \ \ \ \ feftermials。我们的结果概括了Ulas关于案例的最新结果$ M = 1 $和$ d = 1 $。
Let $(r_{A,n}(x))_{n \in \mathbb{N}}$ be a sequence of polynomials with coefficients from a field $K$ satisfying the recurrence relation $r_{A,n}(x)= \sum_{|α|\leq m} t_{α,n}(x)\textbf{r}_{A,n}^α(x)$ of order $d+1 \in \mathbb{N}_{+}$, where $t_{α,n} \in K[x]$, $m \in \mathbb{N}_{+}$ are fixed, $α\in \mathbb{N}^{d+1}$, $|α| = α_0 + \ldots+α_d$ and $\textbf{r}_{A,n}^α(x)=r_{A,n-1}^{α_0}(x)r_{A,n-2}^{α_1}(x)\cdots r_{A,n-d-1}^{α_d}(x).$ We show that under mild assumptions on the initial polynomials $r_{A,0}, \ldots, r_{A,d}$ and the coefficients $t_{α,n}$, we can give the expression for the resultant $\text{Res}(r_{A,n}, r_{A,n-1})$. Our results generalize recent result of Ulas concerning the case $m=1$ and $d=1$.
