An algorithmic approach to discovering and provingq-series identities

An algorithmic method of producingq-series identities from any given power series is discassed. This recursive technique is then used to give new proofs of several classicalq-identities of Gauss and Rogers. Dedicated to the memory of John Knopfmacher, 1937–1999, the inventor of the Engel expansions for q-series. The first author was partially supported by National Science Foundation Grant DMS-9206993 and by The Centre for Applicable Analysis and Number Theory of the University of the Witwatersrand. He wishes to express his gratitude to the second author who provided the hospitality and support which made his participation possible This paper was presented at the fourth International Conference on Average-Case Analysis of Algorithms, Princeton, NJ, by the second author. Online publication September 6, 2000.