An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which
are rational functions. Not only does it decide
conclusively whether there exists a hypergeometric sequence such that
(1)
but actually produces
if it exists. If not, it produces . An outline of the algorithm follows (Petkovšek
et al. 1996):
Petkovšek et al. (1996) describe the algorithm as "one of the landmarks in the history of computerization of the problem of closed form summation."
Gosper's algorithm is vital in the operation of Zeilberger's
algorithm and the machinery of Wilf-Zeilberger
pairs.
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