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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
##### Keywords:
Catalan’s constant; irrationality