A pair of closed form functions (F, G) is said to be a Wilf-Zeilberger pair if F(n + 1, k) - F(n, k) = G(n, k + 1) - G(n, k). The Wilf-Zeilberger formalism provides succinct proofs of known identities and allows new identities to be discovered whenever it succeeds in finding a proof certificate for a known identity. However, if the starting point is an unknown hypergeometric sum, then the Wilf-Zeilberger method cannot discover a closed form solution, while Zeilberger's algorithm can.
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