Geodesic
Estimate of the Lebesgue Function of Fourier Sums in Terms of Modified Meixner Polynomials
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 519-530 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the study of the approximation properties of Fourier sums in terms of the modified Meixner polynomials $m_{n,N}^\alpha(x)$, $n=0,1,\dots$, which generate, for $\alpha>-1$, an orthonormal system on the grid $\Omega_\delta=\{0,\delta,2\delta,\dots\}$ with weight $$ \rho_N(x)=e^{-x}\frac{\Gamma(Nx+\alpha+1)}{\Gamma(Nx+1)} (1-e^{-\delta})^{\alpha+1},\qquad \text{where}\quad \delta=\frac{1}{N},\quad N\ge 1. $$ The main attention is paid to the derivation of a pointwise estimate for the Lebesgue function $\lambda_{n,N}^\alpha(x)$ of Fourier sums in terms of the modified Meixner polynomials for $x\in[\theta_n/2,\infty)$ and $\theta_n=4n+2\alpha+2$.
Keywords: Meixner polynomials, Fourier series
Mots-clés : Lebesgue function. 
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     title = {Estimate of the {Lebesgue} {Function} of {Fourier} {Sums} in {Terms} of {Modified} {Meixner} {Polynomials}},
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R. M. Gadzhimirzaev. Estimate of the Lebesgue Function of Fourier Sums in Terms of Modified Meixner Polynomials. Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 519-530. http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a3/

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