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Some remarks on linear forms containing Catalan’s constant. (Russian) Zbl 1099.11036

The paper deals with the Catalan’s constant \(G=\sum_{n=1}^\infty \frac{(-1)^n}{(2n+1)^2}\). New recurrent sequences of the second order in the form \(r_n=u_nG-v_n\) of the type of Apéry are presented and their asymptotic behavior is proved. The group permutation which is connected with \(G\) is also included. The author concludes that maybe it will be possible to prove the irrationality of the number \(G\) with this tool.

MSC:

11J72 Irrationality; linear independence over a field
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
11B37 Recurrences
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