Wilf-Zeilberger pair

A Wilf-Zeilberger (WZ) pair consists of two related mathematical functions or sequences, called \(F(n, k)\) and \(G(n, k)\), that satisfy a special relation: \[ F(n+1, k) - F(n, k) = G(n, k+1) - G(n, k) \] This relation creates a telescoping effect, allowing complex sums to be simplified or proved automatically. Essentially, WZ pairs are tools for efficiently verifying and discovering identities involving sums and series, particularly in combinatorics and hypergeometric functions. They are fundamental to computer-assisted proof techniques.