Computing the minimal telescoper for sums of hypergeometric terms

Let <i>T</i> (<i>n, k</i>) be a hypergeometric term of <i>n</i> and <i>k.</i> We present in this paper an algorithm to construct the minimal telescoper for <i>U</i> (<i>n, k</i>) = ∑<inf><i>m=b</i></inf><sup><i>n</i>-1</sup> <i>T</i> (<i>m, k</i>), <i>b</i> ε ℤ, if it exists. We show a Maple implementation of this method and discuss the problem of finding closed forms of definite sums of <i>U</i> (<i>n, k</i>).

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