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

##### 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)
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##### References:
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