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A Criterion for the Applicability of Zeilberger's Algorithm to Rational Functions #
 

Summary: A Criterion for the Applicability of
Zeilberger's Algorithm to Rational Functions #
S. A. Abramov
Computer Center of
the Russian Academy of Science
Vavilova 40, Moscow 117967, Russia
abramov@ccas.ru
H. Q. Le
Symbolic Computation Group
University of Waterloo
Waterloo, N2L 3G1, Canada
hqle@scg.math.uwaterloo.ca
Abstract
We consider the applicability (or terminating condition) of the
well­known Zeilberger's algorithm and give the complete solution to
this problem for the case where the original hypergeometric term
F (n, k) is a rational function. We specify a class of identities
# n
k=0 F (n, k) = 0, F (n, k) # C(n, k), that cannot be proven by Zeil­
berger's algorithm. Additionally we give examples showing that the

  

Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

 

Collections: Mathematics; Computer Technologies and Information Sciences