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Russian Mathematical Surveys, 2002, Volume 57, Issue 3, Pages 535–571
DOI: https://doi.org/10.1070/RM2002v057n03ABEH000512 (Mi rm512) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Cyclic graphs and Apéry's theorem

V. N. Sorokin

M. V. Lomonosov Moscow State University
English version PDF (341 kB) Citations (23)
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DOI: https://doi.org/10.1070/RM2002v057n03ABEH000512
Abstract: This is a survey of results about the behaviour of Hermite–Padé approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apéry's result about the irrationality of the value $\zeta(3)$ of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite–Padé problem leads to Apéry's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found.
Received: 15.03.2001
Russian version:
Uspekhi Matematicheskikh Nauk, 2002, Volume 57, Issue 3(345), Pages 99–134
DOI: https://doi.org/10.4213/rm512
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 11M06, 11J72, 41A21, 05C90; Secondary 11J82, 14G10
Language: English
Original paper language: Russian
Citation: V. N. Sorokin, “Cyclic graphs and Apéry's theorem”, Uspekhi Mat. Nauk, 57:3(345) (2002), 99–134; Russian Math. Surveys, 57:3 (2002), 535–571
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
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    Russian version PDF:329
    English version PDF:19
    References:49
    First page:3
     
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