In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate $q$-Bernstein polynomials for a function analytic in the polydisc $D_{R_1}\times D_{R_2}=\{z\in C:|z|<R_1\}\times \{z\in C:\left|z\right|<R_1\}$ for arbitrary fixed $q>1$. We give quantitative Voronovskaja type estimates for the bivariate $q$-Bernstein polynomials for $q>1$. In the univariate case the similar results were obtained by S. Ostrovska: $q$-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution...

A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $\zeta \left(2\right)$ and $\zeta \left(3\right)$, as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers $\zeta \left(5\right)$, $\zeta \left(7\right)$, $\zeta \left(9\right)$, and $\zeta \left(11\right)$ is irrational.