差环中嵌套深度较高的超几何积的表示
Representation of hypergeometric products of higher nesting depths in difference rings
摘要：
提出了一种非平凡的符号机器，它可以在适当设计的差环中对嵌套超几何积的有限集进行算法改写。作为结果，人们得到一个替代的表示在一个单一的产品定义在一个根的单位和嵌套的超几何产品是代数相互独立的。特别地，可以解决零识别问题：嵌套超几何积的输入表达式的值为零，当且仅当输出表达式是零表达式。结合可用的符号求和算法的设置差环，得到一个通用的机器，可以表示（和简化）嵌套产品上定义的嵌套和。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
