Markov's transformation of series and the WZ method

DOI10.1016/j.aam.2004.06.003zbMath1067.65004arXivmath/0405592OpenAlexW1988228156MaRDI QIDQ1775746

Margo Kondratieva, Sergey Yu. Sadov

Publication date: 4 May 2005

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405592

zbMATH Keywords

Hypergeometric seriesWilf-Zeilberger methodConvergence accelerationBasic hypergeometric seriesApéry constantA.A. MarkovDiscrete Green formulaDouble seriesMarkov transformationSeries transformationSr.

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Numerical summation of series (65B10)

Related Items (5)

On a result of Koecher concerning Markov–Apéry-type formulas for the Riemann zeta function ⋮ A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications ⋮ How to Generate All Possible Rational Wilf-Zeilberger Pairs? ⋮ Asymptotic results of the remainders in the series representations for the Apéry constant ⋮ Euler’s constant: Euler’s work and modern developments

Cites Work

• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• Hypergeometric series acceleration via the WZ method
• Computational strategies for the Riemann zeta function
• Well-poised generation of Apéry-like recursions
• The Markov-WZ method
• Faster and faster convergent series for \(\zeta(3)\)
• Rational Functions Certify Combinatorial Identities
• Les lettres de Gh. Hermite à A. Markoff, 1885-1899
• Some families of rapidly convergent series representations for the zeta functions
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