WZ pairs are named after Herbert S. Wilf and Doron Zeilberger, and are instrumental in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series.
A function's WZ counterpart may be used to find an equivalent and much simpler sum.
Although finding WZ pairs by hand is impractical in most cases, Gosper's algorithm provides a method to find a function's WZ counterpart, and can be implemented in a symbolic manipulation program.
A Wilf–Zeilberger pair can be used to verify the identity Divide the identity by its right-hand side: Use the proof certificate to verify that the left-hand side does not depend on n, where Now F and G form a Wilf–Zeilberger pair.
To prove that the constant in the right-hand side of the identity is 1, substitute n = 0, for instance.