All binomial identities are verifiable.
Sister Celine Fasenmyer's technique for obtaining pure recurrence relations for hypergeometric polynomials is formalized and used to show that every identity involving sums of products of binomial coefficients can be verified by checking a finite number of its special cases.
Zeilberger
D
D
Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel.