Jackson-type theorem on approximation by algebraic polynomials in the uniform metric with Laguerre weight

I. I. Sharapudinov, when studying the approximation properties of partial sums of a special series in Laguerre polynomials, introduced a weighted best approximation characteristic $E_n(f,u_r)$ that depends on a parameter $r$. In the present paper, we prove a Jackson-type theorem for this characteristic for $r=1$.