Geodesic
Approximation of discrete functions using special series by modified Meixner polynomials
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 395-405.

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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 $\theta_n=4n+2\alpha+2$.
Keywords: Meixner polynomials, Fourier series, special series
Mots-clés : Lebesgue function. 
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R. M. Gadzhimirzaev. Approximation of discrete functions using special series by modified Meixner polynomials. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 395-405. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a127/

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