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The Markov-WZ Method

2004; Electronic Journal of Combinatorics; Volume: 11; Issue: 1 Linguagem: Inglês

10.37236/1806

1097-1440

Mohamud Mohammed, Doron Zeilberger,

Fractional Differential Equations Solutions

Andrei Markov's 1890 method for convergence-acceleration of series bears an amazing resemblance to WZ theory, as was recently pointed out by M. Kondratieva and S. Sadov. But Markov did not have Gosper and Zeilberger's algorithms, and even if he did, he wouldn't have had a computer to run them on. Nevertheless, his beautiful ad-hoc method, when coupled with WZ theory and Gosper's algorithm, leads to a new class of identities and very fast convergence-acceleration formulas that can be applied to any infinite series of hypergeometric type.