Andrei Markov’s 1890 beautiful ad-hoc method of transforming a series of hypergeometric type into a rapidly-converging series was upgraded recently to a full-fledged method by Mohammed and Zeilberger, but only for the ordinary case. In this article, the q-case is developed and it is shown how Markov’s ad-hoc method, when coupled with q-WZ theory and q-Gosper’s algorithm, leads to a new class of identities and very fast convergence-acceleration series that can be applied to any infinite series of q-hypergeometric type.
AMS Subject Classification.05A10 05A19 33F10 33C20 33-04
Keywords.WZ theory series convergence q-hypergeometric q-Gosper’s algorithm q-Zeilberger’s algorithm
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