MultiSum

A Mathematica Package for Proving Hypergeometric Multi-Sum Identities

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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.

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]