On the existence of telescopers for rational functions in three variables. (May 2021) - Chen, Shaoshi; Du, Lixin; Wang, Rong-Hua; Zhu, Chaochao
Abstract: Zeilberger's method of creative telescoping is crucial for the computer-generated proofs of combinatorial and special-function identities. Telescopers are linear differential or ( q -)recurrence operators computed by algorithms for creative telescoping. Two fundamental problems related to creative telescoping are whether telescopers exist, and how to construct them efficiently when they do. In this paper, we solve the existence problem of telescopers for rational functions in three variables including 18 cases. We reduce the existence problem from the trivariate case to the bivariate case and some related problems. The existence criteria given in this paper enable us to determine the termination of algorithms for creative telescoping with trivariate rational inputs.