A new Sigma approach to multi-summation. (English) Zbl 1078.33021
The author presents a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products but also over \(\partial\)-finite and holonomic summand expressions that are given by a linear recurrence. For this approach a new Package Sigma for the computer algebra system Mathematica is presented.
Reviewer: Hans Benker (Merseburg)
MSC:
| 33F05 | Numerical approximation and evaluation of special functions |
| 68W30 | Symbolic computation and algebraic computation |
| 05E35 | Orthogonal polynomials (combinatorics) (MSC2000) |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
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