Geodesic
On a refinement of the asymptotic formula for the Lebesgue constants
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 180-186.

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For the Lebesque constant of the classical Lagrange polynomial defined in the even number of nodes of interpolation, strict two-sided estimation is received. On this basis, an undefined value $O(1)$ is refined in the well-known asymptotic equality for the Lebesque constant. Two actual problems in the interpolation theory associated with the optimal choice of $O(1)$ are solved. 
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I. A. Shakirov. On a refinement of the asymptotic formula for the Lebesgue constants. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 180-186. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a7/

[1] Goncharov V. L., Interpolation theory and approximations of functions, GTTI, M.–Leningrad, 1934 (in Russian)

[2] Natanson I. P., Constructive function theory, v. 1–3, F. Ungar Publ. Co., New York, 1964–1965 | Zbl

[3] Stechkin S. B., Subbotin Yu. N., Splins in computational mathematics, Nauka, M., 1976 (in Russian) | MR

[4] Korneichuk N. P., Constants in approximation theory, Nauka, M., 1987 (in Russian) | MR

[5] Dzyadyk V. K., Approximation Methods for solving Differential and Integral Equations, Naukova Dumka, Kiev, 1988 (in Russian) | MR

[6] Privalov A. A., Interpolation of functions theory, Saratov Univ. Press, Saratov, 1990 (in Russian) | MR

[7] Shakirov I. A., “About the fundamental characteristics of the lagrange interpolation polynomials family”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:1(2) (2013), 99–104 (in Russian)

[8] Gabdulhaev B. G., Optimal approximations of linear problems solutions, Kazan Univer. Press, Kazan, 1980 (in Russian) | MR

[9] Babenko K. I., Fundamentals of numerical analysis, NIC Regular and chaotic dynamics, M.–Izhevsk, 2002 (in Russian)

[10] Brutman L., “Lebesgue functions for polynomial interpolation — a survey”, Ann. Numer. Math., 4 (1997), 111–127 | MR | Zbl

[11] Vertesi P., “On the Lebesgue function and Lebesgue constant : a tribute to Paul Erdos”, Bolyai Society of Mathematical Studies, 11, 2002, 705–728 | MR | Zbl