On Catalan's constant (Q2631147)

The author applies a new interesting method to prove the following result on Catalan's constant \(G=\sum^\infty_{k=0} (-1)^k/(2k+1)^2= 0.91596\dots\). {\parindent=6mm \begin{itemize}\item[1)]There exists an efficient construction of an infinite sequence of rational numbers \(p/q\) satisfying the inequality \(0<|G-p/q|< 1/\sqrt{q}\). \item[2)] To construct the next approximation \(p/q\), one needs \(0(\ln^2q)\) arithmetic operations. We note that the irrationality of the constant \(G\) is not proved up to now. \end{itemize}}