Gosper's algorithm

Summary

Gosper's algorithm decides, for a hypergeometric term $t_k$, whether its partial sums $\sum_{j < k} t_j$ are a hypergeometric term plus a constant. When they are, it finds that term. This is the discrete analogue of deciding whether an integral can be done in closed form. It reduces the question to finding a polynomial solution of a linear recurrence with polynomial coefficients. It is a building block of Zeilberger's algorithm and of the search for WZ pairs.