Zeilberger's algorithm

Summary

Zeilberger's algorithm, also called the method of creative telescoping, takes a definite sum $f(n) = \sum_k F(n, k)$ of a hypergeometric term. It finds a linear recurrence in $n$ with polynomial coefficients that $f$ satisfies. It works by running a parametrised version of Gosper's algorithm on a combination of shifts $F(n + j, k)$. With the recurrence and a few initial values, identities for definite sums can be proved or discovered automatically. It is a main tool of the "A = B" approach to hypergeometric identities.