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ISSN 0361-7688, Programming and Computer Software, 2008, Vol. 34, No. 4, pp. 187190. Pleiades Publishing, Ltd., 2008. 1 1. INTRODUCTION
 

Summary: ISSN 0361-7688, Programming and Computer Software, 2008, Vol. 34, No. 4, pp. 187­190. © Pleiades Publishing, Ltd., 2008.
187
1 1. INTRODUCTION
The object of this note is to present the results of [1]
related to the so-called "bottom summation" in a sim-
pler form. The object of our investigation is correctness
of the discrete Newton­Leibniz formula for definite
summation in the case where a summing operator has
been successfully constructed by the Accurate Summa-
tion algorithm [2] or by Gosper's algorithm [3]. In the
detailed proofs given in [1], many abstract notions were
used. In addition, it was necessary to prove a number of
auxiliary statements. As a result, the paper [1] is quite
difficult to read. However, the main results of [1] are of
some practical interest for computer algebra and their
short presentation without complicated proofs can be
useful.
Below, we present the main results of [1] in a sim-
pler form and give some illustrations. Full proofs can be
found in [1].

  

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

 

Collections: Mathematics; Computer Technologies and Information Sciences