WZ-style certification and sister celine's technique for abel-type sums

Abstract

In 1992 Herbert Wilf and Doron Zeilberger showed how Sister Celine's technique could be used to establish the certification procedure for proper-hypergeometric summations in one variable. The basis of the procedure depends on showing that every proper-hypergeometric term Fph (n, k) satisfied some nontrivial k-free recurrence. In this paper we extend Sister Celine's technique to the more general Abel-type terms. In doing so, we extend the applicability of the certification procedure from an already large class of sums to an even larger set of sums. Several examples are given, one of them a generalization of Abel's identity which is itself a generalization of the famous binomial coefficient identity.