A new Sigma approach to multi-summation

We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr, 1981), but also over ∂-finite and holonomic summand expressions that are given by a linear recurrence. This approach implies new computer algebra tools implemented in Sigma to solve multi-summation problems efficiently. For instance, the extended Sigma package has been applied successively to provide a computer-assisted proof of Stembridge's TSPP Theorem.