qZeil: A Mathematica implementation of q-analogues of Gosper’s and Zeilberger’s algorithm

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.

Author

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

  • RiesePhD.nb a Mathematica notebook consisting of the examples from Riese’s thesis in slightly modified form matching the syntax of the newest version of the package

Literature

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]