We extend the criterion on the existence of telescopers for hypergeometric terms to the case of P-recursive sequences. This criterion is based on the concept of integral bases and the generalized Abramov-Petkovsek reduction for P-recursive sequences.

翻译：我们将超几何项望远镜子存在性的判定准则推广至P-递归序列情形。该准则建立在积分基概念及针对P-递归序列的广义Abramov-Petkovsek约化方法基础之上。