On the Existence of Telescopers for Mixed Hypergeometric Terms
  We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed hypergeometric inputs. 
Shaoshi Chen, Fr\'ed\'eric Chyzak, Ruyong Feng, Guofeng Fu, Ziming Li
cs.SC math.CO