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A Computer Proof of a Polynomial Identity Implying a Partition Theorem of Göllnitz

Alexander Berkovich
Organization: Pennsylvania State University
Axel Riese
Organization: Johannes Kepler University
Department: Research Institute for Symbolic Computation
Journal / Anthology

Advances in Applied Mathematics
Year: 2002
Volume: 28
Page range: 1-16

In this paper we give a comuter proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we rovide computer proofs for new finite analogs of Jacobi and Euler formulas. All computer proofs are done with the aid of the new computer algebra package qMultiSum developed by the second author. qMultiSum implements an algorithmic refinement of Wilf and Zeilberger's multi-q-extension of Sister Celine's technique utilizing additional ideas of Verbaeten and Wegschaider.

*Mathematics > Calculus and Analysis > Special Functions
*Mathematics > Discrete Mathematics > Combinatorics

Göllnitz's theorem, Jacobi and Euler functions, computer proof