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 ζ(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.
This publication is cited in the following 23 articles:
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A. P. Starovoitov, “On asymptotic form of the Hermite–Pade approximations for a system of Mittag-Leffler functions”, Russian Math. (Iz. VUZ), 58:9 (2014), 49–56
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, “On q q -analogues of two-one formulas for multiple harmonic sums and multiple zeta star values”, Monatsh Math, 2014
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A. P. Starovoitov, “Approksimatsii Ermita–Pade dlya sistemy funktsii Mittag-Lefflera”, PFMT, 2013, no. 1(14), 81–87
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