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Telescoping in the Context of Symbolic Summation in Maple

Summary: Telescoping in the Context of Symbolic
Summation in Maple
S.A. Abramov a,1 , J.J. Carette b , K.O. Geddes c,2 , H.Q. Le c,#,3
a Dorodnicyn Computing Centre, Russian Academy of Science,
Vavilova st. 40, 119991, Moscow, GSP­1, Russia
b Computing and Software, McMaster University, Hamilton, L8S 4L8, Canada
c Symbolic Computation Group, School of Computer Science,
University of Waterloo, Waterloo, N2L 3G1, Canada
This paper is an exposition of di#erent methods for computing closed forms of def­
inite sums. The focus is on recently­developed results on computing closed forms of
definite sums of hypergeometric terms. A design and an implementation of a soft­
ware package which incorporates these methods into the computer algebra system
Maple are described in detail.
1 Introduction
In order to compute closed forms of definite sums, one can apply one of at
least three methods: the classical telescoping method, the creative telescoping
method, or the conversion method. The classical telescoping method is based
on the computation of an anti­di#erence of the input summand T , or on the
# Corresponding author.


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


Collections: Mathematics; Computer Technologies and Information Sciences