A criterion for the applicability of Zeilberger's algorithm to rational functions
The applicability of Zeilberger's algorithm is considered and complete solutions are given for the case where the original hypergeometric term \(F(n,k)\) is a rational function. A class of identities \(\sum_{k=0}^n F(n,k)=0\) is specified that cannot be proven by Zeilberger's algorithm. Examples are discussed showing that the set of hypergeometric terms on which Zeilberger's algorithm terminates is a proper subset of the set of all hypergeometric terms, but a super-set of the set of proper terms. The algorithms are compared with existing Maple codes.
scientific article; zbMATH DE number 1882138