MultiSum: A Mathematica package for proving hypergeometric multi-sum identities

This package is part of the RISCErgoSum bundle. See Download and Installation.

Short Description

MultiSum is a Mathematica package for proving hypergeometric multi-sum identities. It uses an efficient generalization of Sister Celine’s technique to find a homogeneous polynomial recurrence relation for the sum.

The package has been developed by `Kurt Wegschaider`_, a former member of the RISC Combinatorics group.

Authors

  • Kurt Wegschaider
  • Axel Riese

Accompanying Files

Literature

A detailed description of the package and of the method (a generalization of Sister Celine’s technique) together with several examples is contained in the diploma thesis

  • K. Wegschaider, Computer Generated Proofs of Binomial Multi-Sum Identities, Diploma Thesis, RISC, J. Kepler University, Linz, May 1997. [ps]

A more recent version of the implementation with its latest enhancements is described by means of an example in the paper

  • R. Lyons, P. Paule, and A. Riese, A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers, Appl. Algebra Engrg. Comm. Comput., 13 (2002), 327-333. [pdf] [original via SpringerLink]