Two hypergeometric tales and a new irrationality measure of \(\zeta (2)\). (English) Zbl 1307.11085

Zudilin, Wadim

Ann. Math. Qué. 38, No. 1, 101-117 (2014).

The author proves that the irrationality exponent of the number \(\zeta(2)=\pi^2/6\) is bounded from above by \(5.09541178\). He also proves several identities for hypergeometric integrals which include the number \(\zeta(2)\). The proof is not simple and requires some knowledge from the theory of the hypergeometrical functions.

Reviewer: Jaroslav Hančl (Ostrava)

MSC:

11J82	Measures of irrationality and of transcendence
11Y60	Evaluation of number-theoretic constants
33C20	Generalized hypergeometric series, \({}_pF_q\)
33C60	Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)

Keywords:

irrationality exponent; rational approximations; hypergeometric series

References:

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