We present criteria on the existence of telescopers for trivariate rational functions in four mixed cases, in which discrete and continuous variables appear simultaneously. We reduce the existence problem in the trivariate case to the exactness testing problem, the separation problem and the existence problem in the bivariate case. The existence criteria we present help us determine the termination of Zeilberger's algorithm for the input functions studied in this paper.

中文翻译：

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代数函数的惰性Hermite缩减和创造性伸缩

我们提出了在四种混合情况下离散变量和连续变量同时出现的三元有理函数望远镜的存在性标准。我们将三变量情况下的存在性问题简化为准确性检验问题，分离问题和双变量情况下的存在性问题。我们提出的存在性准则有助于确定本文研究的输入函数的Zeilberger算法的终止。