Markov's transformation of series and the WZ method

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Abstract

In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the Wilf–Zeilberger (WZ) method. We review Markov's work, put it in the context of modern computer-aided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.

Keywords

Wilf–Zeilberger method
A.A. Markov, Sr.
Series transformation
Convergence acceleration
Hypergeometric series
Basic hypergeometric series
Double series
Discrete Green formula
Apéry constant

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