Simplifying Sums in Πς ∗ - Extensions Carsten

We present telescoping algorithms which compute optimal sum representations of indefinite nested sums. More precisely, given a rational summand expression in terms of nested sums and products, the algorithm splits the summand into a summable part, which can be summed by telescoping, and into a non-summable part, which is degree-optimal with respect to one of the most nested sums or products. If possible, all the most nested sums and products can be eliminated in the non-summable part. We illustrate our summation algorithms by various concrete examples.