论文标题
关于$π\mathbfς^*$ - 字段扩展的线性普通差方程的有理几何解决方案
On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in $Π\mathbfΣ^*$-field extensions
论文作者
论文摘要
我们提出了一种完整的算法，该算法计算$πς^*$ - 字段中的参数化线性差方程的均质线性差方程的所有高几何解和参数化线性差方程的合理解决方案。更笼统地，我们为一个$πς^*$ - 字段扩展的塔楼构建的大量差异字段提供了一个灵活的框架，该框架在满足某些算法属性的差异字段上扩展。结果，人们可以根据不确定的嵌套总和和在参数化线性差方程的组件内计算所有解决方案，并且可以找到在同质线性差方程的出现的总和和产物上定义的所有超几何溶液。
We present a complete algorithm that computes all hypergeometric solutions of homogeneous linear difference equations and rational solutions of parameterized linear difference equations in the setting of $ΠΣ^*$-fields. More generally, we provide a flexible framework for a big class of difference fields that is built by a tower of $ΠΣ^*$-field extensions over a difference field that satisfies certain algorithmic properties. As a consequence one can compute all solutions in terms of indefinite nested sums and products that arise within the components of a parameterized linear difference equation, and one can find all hypergeometric solutions that are defined over the arising sums and products of a homogeneous linear difference equation.
