WZ theory

Summary

WZ theory, named after Herbert Wilf and Doron Zeilberger, is a method to prove identities of the form $\sum_k F(n, k) = 1$ by computer, see the definition. The proof consists of one rational function, the WZ certificate. The certificate turns $F$ into a Wilf–Zeilberger pair, whose defining equation can be checked by algebra alone. It applies to sums of hypergeometric terms, such as most identities for binomial coefficients, and it relates to Zeilberger's algorithm and Gosper's algorithm.