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Ramanujan-type formulae and irrationality measures of some multiples of $\pi$

W. V. Zudilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: An explicit construction of simultaneous Padé approximations for generalized hypergeometric series and formulae for the quantities $\pi\sqrt d$, $d\in\{1,2,3,10005\}$, in terms of these series are used for estimates of irrationality measures of these multiples of $\pi$. Other possible applications are also discussed.

UDC: 511.36+517.5

MSC: Primary 11J82, 41A2; Secondary 33C20

Received: 18.08.2004

DOI: 10.4213/sm1376

 English version: Sbornik: Mathematics, 2005, 196:7, 983–998

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