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Gosper's Algorithm, Accurate Summation, and the Discrete NewtonLeibniz Formula #
 

Summary: Gosper's Algorithm, Accurate Summation,
and the Discrete Newton­Leibniz Formula #
S. A. Abramov +
Russian Academy of Sciences
Dorodnicyn Computing Centre
Vavilova 40, 119991, Moscow GSP­1, Russia
sabramov@ccas.ru
M. PetkovŸsek #
Department of Mathematics
University of Ljubljana
Jadranska 19, SI­1000 Ljubljana, Slovenia
Marko.Petkovsek@fmf.uni­lj.si
ABSTRACT
Su#cient conditions are given for validity of the discrete
Newton­Leibniz formula when the indefinite sum is obtained
either by Gosper's algorithm or by Accurate Summation al­
gorithm. It is shown that sometimes a polynomial can be
factored from the summand in such a way that the safe sum­
mation range is increased.
Categories and Subject Descriptors: G.2.1 [Combina­

  

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

 

Collections: Mathematics; Computer Technologies and Information Sciences