A Mathematica Implementation of q-Analogues of Gosper's and Zeilberger's Algorithm


Software URL

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

Short Description

qZeil is a Mathematica implementation of q-analogues of Gosper’s and Zeilberger’s algorithm for proving and finding indefinite and definite q-hypergeometric summation identities. The package has been developed by Axel Riese, a former member of the RISC Combinatorics group.

Accompanying Files

  • WhatsNew.txt an ASCII-documentation of all changes and new features since version 1.4
  • qZeilExamples.nb a Mathematica notebook consisting of about 500 examples


Information on the installation and use of the package (together with its theoretical background) can be found in the paper
  • P. Paule and A. Riese, A Mathematica q-Analogue of Zeilberger’s Algorithm Based on an Algebraically Motivated Approach to q-Hypergeometric Telescoping, in Special Functions, q-Series and Related Topics, Fields Inst. Commun., Vol. 14, pp. 179-210, 1997. [pdf]
Moreover, an up-to-date manual for the package is presented in Riese’s Ph.D. thesis
  • A. Riese, Contributions to Symbolic q-Hypergeometric Summation, Ph.D. Thesis, RISC, J. Kepler University, Linz, 1997. [pdf]