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The q-Markov-WZ Method
Mohamud Mohammed
Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA
mohamudm@math.rutgers.edu
Annals of Combinatorics 9 (2) p.205-221 June, 2005
AMS Subject Classification: 05A10, 05A19, 33F10, 33C20, 33-04
Abstract:
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-fiedged 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.
Keywords: WZ theory, series convergence, q-hypergeometric, q-Gosper's algorithm, q-Zeilberger's algorithm

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