Gosper's Algorithm and Accurate Summation as Definite Summation Tools

S. A. Abramov, M. Petkovsek


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 inreased.