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Background information.
Identities
that involve hypergeometric series play an important role in
various branches of modern mathematics. It turns out, that one can
discover new identities of this type and prove existing identities in a
completely algorithmic fashion. First complete algorithm for doing this
was developed early in 1990 by professor Herbert Wilf (University of
Pennsylvania) and professor Doron Zeilberger (Rutgers
University). They called it WZ method in honor of two famous complex
variables. A great introduction toWZ theory can be downloaded here free of charge. A
crucial step in WZ-type proof of a given identity is one that involves
finding a certain rational function R which is unique for every
identiity. To find this function, WZ method uses algorithm developed by
R.J. Gosper. Because use of Gosper's algorithm can be very time- and
memory-consuming, many important identities still cannot be proven
using WZ method. The goal of my REU research project was to develop
new, faster and more efficient method for finding function R.
Final presentation of our results can be found here.
We implemented our method as Maple package; it can be downloaded
from here.
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