论文标题
西格尔决定因素的类似物
An analogue of Siegel's determinant
论文作者
论文摘要
$ e $ functions的siegel-shidlovskii理论涉及与线性形式$ d^kr（t）$的确定因素的非逐渐证明，这是辅助函数$ r（t）$的衍生物。令非零函数$ f（t）$满足$ m $ th订单线性微分方程，我们将使用差分运算符$δ= td $编写，让$ l（t）$为任何非零线性形式$Δ^i f（t）$（t）$（t）$（i = 0，...，...，...，m-1，m-1; m-1; m-1; m \ ge 2）$。 $ \ det \ det \ Mathcal a_k $附加到线性形式的$δ^kl（t）$具有某些简单属性，使我们可以简短证明$ \ det \ det \ det \ nathcal a_k $，用于一类差分方程的类别的差异方程，包括超级差异方程的A子类别。
Siegel-Shidlovskii theory of $E$-functions involves a non-vanishing proof for the determinants attached to the linear forms $D^kR(t)$, derivatives of an auxiliary function $R(t)$. Let a non-zero function $F(t)$ satisfy $m$th order linear differential equation which we shall write using the differential operator $Δ=tD$ and let $L(t)$ be any non-zero linear form of the derivatives $Δ^i F(t)$ $(i=0,...,m-1; m\ge 2)$. The determinants $\det\mathcal A_k$ attached to the linear forms $Δ^kL(t)$ have certain simple properties that allow us to give a short proof for the non-vanishing of $\det\mathcal A_k$ for a class of differential equations including a subclass of hypergeometric differential equations.
