Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Sultanov E. S. Limit Discrete Meixner Series and Their Approximative Properties. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 1, pp. 29-32. DOI: 10.18500/1816-9791-2013-13-1-1-29-32, EDN: SMXXGR

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.02.2013
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Russian
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SMXXGR

Limit Discrete Meixner Series and Their Approximative Properties

Autors: 
Sultanov Emir Sherifovich, Daghestan Scientific Centre of Russian Academy of Sciences
Abstract: 

In this article the problemof function approximation by discrete series by Meixner polynomials orthogonal on uniform net {0, 1, . . .} is investigated. We constructed new series by these polynomials for which partial sums coincidewith input function f(x) in x = 0. These new series were constructed by the passage to the limit of Fourier series Σk=0∞fαkmαk(x) by Meixner polynomials when α → −1.

References: 
  1. Meixner J. Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Function // J. of the London Math. Soc. 1934. Vol. 9. P. 6–13.
  2. Шарапудинов И. И. Смешанные ряды по ортогональным полиномам. Теория и приложения. Махачкала : Дагестан. науч. центр РАН, 2004. 276 с. [Sharapudinov I. I. Mixed series of orthogonal polynomials. Theory and applications. Makhachkala : Dagestan Scientific Center of RAS, 2004. 276 p.]
Received: 
17.08.2012
Accepted: 
10.01.2013
Published: 
15.02.2013