Geodesic
Approximation of functions defined on the grid $\{0, \delta, 2\delta, \ldots\}$ by Fourier-Meixner sums
Daghestan Electronic Mathematical Reports, no. 7 (2017), pp. 61-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper is devoted to the study of approximation properties of partial sums of the Fourier series in the modified Meixner polynomials $M_{n,N}^\alpha(x)=M_n^\alpha(Nx)$ $(n=0, 1, \dots)$ which for $\alpha>-1$ constitute an orthogonal system on the grid $\Omega_{\delta}=\{0, \delta, 2\delta, \ldots\}$, where $\delta=\frac{1}{N}$, $N>0$ with weight $w(x)=e^{-x}\frac{\Gamma(Nx+\alpha+1)}{\Gamma(Nx+1)}$. The main attention is paid to obtaining an upper estimate for the Lebesgue function of these partial sums.
Keywords: Meixner polynomials, Fourier series
Mots-clés : Lebesgue function. 
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     author = {R. M. Gadzhimirzaev},
     title = {Approximation of functions defined on the grid $\{0, \delta, 2\delta, \ldots\}$ by {Fourier-Meixner} sums},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {61--65},
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R. M. Gadzhimirzaev. Approximation of functions defined on the grid $\{0, \delta, 2\delta, \ldots\}$ by Fourier-Meixner sums. Daghestan Electronic Mathematical Reports, no. 7 (2017), pp. 61-65. http://geodesic.mathdoc.fr/item/DEMR_2017_7_a6/

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