Section: New Results

Criterion for the existence of telescopers for mixed hypergeometric terms

Creative telescoping is a process that determines a univariate recurrence satisfied by the sum of a summand described by a system of bivariate recurrences. For hypergeometric summands, that is, summands given by first-order linear recurrences, this has led to Zeilberger's algorithm in the early 1990s, since then followed by a large number of works, including a natural counterpart for integration. The history of creative-telescoping algorithms was surveyed this year in Chyzak's HDR [1] . Also this year, we presented in [6] a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on additive and multiplicative decompositions. The criterion had enabled us to determine the termination of Zeilberger's algorithms for mixed hypergeometric inputs prior to any costly computations, and to verify that certain indefinite sums do not satisfy any polynomial differential equation.