The Markov-WZ Method
نویسندگان
چکیده
منابع مشابه
The Markov-WZ Method
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, lead...
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By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher’s and Almkvist-Granville’s Apéry-like formulae for odd zeta values. As a consequence, we get a new identity producing Apéry-like series for all ζ(2n+ 4m+ 3), n,m ≥ 0, convergent at the geometric rate with ratio 2−10.
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متن کاملun 2 00 4 Markov ’ s Transformation of Series and the WZ Method
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 WilfZeilberger (WZ) method. We review Markov’s work, put it in the context of modern computeraided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.
متن کامل3 1 M ay 2 00 4 Markov ’ s Transformation of Series and the WZ Method
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 WilfZeilberger (WZ) method. We review Markov’s work, put it in the context of modern computeraided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2004
ISSN: 1077-8926
DOI: 10.37236/1806