A report on Zeilberger's algorithm.


February 9th, 2005 at 4:00pm in K9509.


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.