... existence and the implementation of the algorithm. The existence of a recurrence of the form (6.1.3) for the summand F (n, k)isassured, under the same hypotheses as those of Theorem 4.4.1 (the FundamentalTheorem), ... example, the problem of indefinite integration104 Zeilberger’s Algorithmin the Liouvillian sense, and the question of indefinite hypergeometric summation,viz., the class of famous questions of classical ... for the fast discovery of the recurrence for aproper hypergeometric term, in the telescoped form (6.1.3). The algorithmic imple-mentation makes strong use of the existence, but not of the method...