Engel Expansions of q-Series by Computer Algebra

The q-Engel Expansion is an algorithm that leads to unique series expansions of qseries. Various examples related to classical partition theorems, including the RogersRamanujan identities together with the elegant generalization found by Garrett, Ismail and Stanton, have been described recently. The object of this paper is to present the computer algebra package Engel, written in Mathematica, that has already played a significant rôle in this work. The package now is made freely available via the web and should help to intensify research in this new branch of q-series theory. Among various ∗Partially supported by National Science Foundation Grant DMS-9206993. †Partially supported by SFB grant F1305 of the Austrian FWF and by the Centre for Applicable Analysis and Number Theory of the University of Witwatersrand. ‡Supported by SFB grant F1305 of the Austrian FWF.