A Mathematica Version of Zeilbergerʹs Algorithm for Proving Binomial Coefficient Identities

Based on Gosperʹs algorithm for indefinite hypergeometric summation, Zeilbergerʹs algorithm for proving binomial coefficient identities constitutes a recent breakthrough in symbolic computation. Mathematica implementations of these algorithms are described. Nontrivial examples are given in order to illustrate the usage of these packages which are available by e-mail request to the first-named author.