Cite this article as:

Sultanov E. S. Limit Discrete Meixner Series and Their Approximative Properties. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 1, pp. 29-32. DOI: https://doi.org/10.18500/1816-9791-2013-13-1-1-29-32

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.518.82

Limit Discrete Meixner Series and Their Approximative Properties

Authors: 
Sultanov Emir Sherifovich, Daghestan Scientific Centre of the Russian Academy of Sciences, Makhachkala, Russia, Russia, 367025, Makhachkala, M. Gadjieva st., 45 , emir.sultanov@gmail.com
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.

Key words: 
Meixner polynomials, Fourier series, limit series
DOI: 
https://doi.org/10.18500/1816-9791-2013-13-1-1-29-32
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.]
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