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.

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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/

[1] I. I. Sharapudinov, Mnogochleny, ortogonalnye na setkakh, Makhachkala, Izd-vo Dagestanskogo gos. ped. un-ta, 1997

[2] R. M. Gadzhimirzaev, “Approximative properties of Fourier-Meixner sums”, Probl. Anal. Issues Anal., 7(25):1 (2018), 23–40 | DOI | MR

[3] Z. D. Gadzhieva, Smeshannye ryady po polinomam Meiksnera, Dis. $\dots$ kand. fiz.-matem. nauk, Saratovskii gos. un-t, Saratov, 2004

[4] A. F. Nikiforov, S. K. Suslov, V. B. Uvarov, Klassicheskie ortogonalnye mnogochleny diskretnoi peremennoi, M., Nauka, 1985 | MR

[5] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Spravochnaya matematicheskaya biblioteka, Nauka, M., 1974 | MR | Zbl

[6] R. M. Gadzhimirzaev, “Priblizhenie funktsii, zadannykh na setke $\{0, \delta, 2\delta, \ldots\}$ summami Fure-Meiksnera”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 61–65 | DOI