A report on Zeilberger's algorithm.
Ha Le, MITACS/CECM
Abstract: Zeilberger's algorithm, also known as the method of creative telescoping, has been shown to be a very useful tool in a wide range of applications. These include finding closed forms of definite sums of hypergeometric terms, certifying large classes of identities in combinatorics and in the theory of special functions. Despite the extensive work on the algorithm, there still exist many interesting problems arising out of the algorithm. In this talk, we review Zeilberger's algorithm, and address two key problems: (1) the limitations in the domain of applicability of Zeilberger's algorithm, and (2) the efficiency of the algorithm. We also provide a sketch of the algorithms which help solve or alleviate these problems.