Approximation of discrete functions using special series by modified Meixner polynomials

This article is devoted to the study of approximative properties of the special series by modified Meixner polynomials $M_{n,N}^\alpha(x)$ $(n=0, 1, \dots)$. For $\alpha>-1$ these polynomials form an orthogonal system on the grid $\Omega_{\delta}=\{0, \delta, 2\delta, \ldots\}$ with respect to the weight function $w(x)=e^{-x}\frac{\Gamma(Nx+\alpha+1)}{\Gamma(Nx+1)}$, where $\delta=\frac{1}{N}$, $N>0$. We obtained upper estimate on $\left[\frac{\theta_n}{2},\infty\right)$ for the Lebesgue function of partial sums of a special series, where $\theta_n=4n+2\alpha+2$.