... s + 1), completing the proof.There is another way of proving the induction step which does not need Gosper’salgorithm, namely taking the difference of f(n, s) w.r.t. n and showing that it isequal ... 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), ... together with Petkovˇsek’s algorithms, placed in the elite class that contains, for example, the problem of indefinite integration104 Zeilberger’s Algorithm in the Liouvillian sense, and the...