Quadratic irrationality exponents of some numbers / A. A. Polyanskii. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 5. P. 25-29 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

The paper presents upper estimates for the non-quadraticity measure of the numbers √(2k+1) ln ((k+1-√(2k+1))/k) and √(2k-1) arctg (√(2k-1))/(k-1))), where k ∈ N. In particular, we improved an upper estimate for the non-quadraticity measure of $\ln 2$.

Key words: non-quadraticity measure.