Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula
Sergei A. Abramov, M. Petkovšsek · 2005
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.