论文标题
差环中较高嵌套深度的高几何产物的表示
Representation of hypergeometric products of higher nesting depths in difference rings
论文作者
论文摘要
提出了一种非平凡的符号机制，可以在适当设计的差环中以有限的嵌套超几何产物为有限的算法。结果，一个人以一种在统一和嵌套超几何产物的根部定义的单个产品来获得替代表示，这些产品彼此之间在代数上是独立的。特别是，人们可以解决零识别问题：嵌套超几何产物的输入表达在且仅当输出表达式为零时，将其评估为零。结合可用的符号求和算法在差环的设置中，获得了可以代表（和简化）嵌套产品定义的嵌套总和的通用机械。
A non-trivial symbolic machinery is presented that can rephrase algorithmically a finite set of nested hypergeometric products in appropriately designed difference rings. As a consequence, one obtains an alternative representation in terms of one single product defined over a root of unity and nested hypergeometric products which are algebraically independent among each other. In particular, one can solve the zero-recognition problem: the input expression of nested hypergeometric products evaluates to zero if and only if the output expression is the zero expression. Combined with available symbolic summation algorithms in the setting of difference rings, one obtains a general machinery that can represent (and simplify) nested sums defined over nested products.
