Geodesic
Lebesgue functions corresponding to a~family of Lagrange interpolation polynomials
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 77-89

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In this paper we obtain various explicit forms of the Lebesgue function corresponding to a family of Lagrange interpolation polynomials defined at an even number of nodes. We study these forms by using the derivatives up to the second order inclusive. We estimate exact values of Lebesgue constants for this family from below and above in terms of known parameters. In a particular case we obtain new simple formulas for calculating these estimates.
Mots-clés : Lagrange interpolation polynomials, Lebesgue functions and constants
Keywords: generalized Dirichlet kernel. 
@article{IVM_2013_7_a6,
     author = {I. A. Shakirov},
     title = {Lebesgue functions corresponding to a~family of {Lagrange} interpolation polynomials},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {77--89},
     publisher = {mathdoc},
     number = {7},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_7_a6/}
}
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I. A. Shakirov. Lebesgue functions corresponding to a~family of Lagrange interpolation polynomials. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 77-89. http://geodesic.mathdoc.fr/item/IVM_2013_7_a6/