Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula

Authors:
S. A. Abramov;M. Petkovšsek
Affiliations:
Russian Academy of Sciences, Moscow, Russia;University of Ljubljana, Ljubljana, Slovenia
Venue:
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Year:
2005

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Abstract

Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper's algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is increased.