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Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 2, Pages 58–72 (Mi vmj617)  

This article is cited in 3 scientific papers (total in 3 papers)

Difference equations and Sobolev orthogonal polynomials, generated by Meixner polynomials

I. I. Sharapudinovab, Z. D. Gadzhievacb, R. M. Gadzhimirzaevc

a Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
b Daghestan State Pedagogical University
c Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala

Abstract: The representation of the Cauchy problem's solution for a difference equation with variable coefficients and given initial conditions at $x = 0$ by expanding this solution in a Fourier series on Sobolev polynomials orthogonal on the grid $(0,1,\ldots)$. The representation is based on contraction new polynomials orthogonal on Sobolev and generated by classical Meixner's polynomials. For new polynomials an explicit formula containing Meixner polynomials is obtained. This result allows us to investigate the asymptotic properties of new polynomials orthogonal on Sobolev on the grid $(0,1, \ldots)$ with a given weight. In addition, it allows to solve the problem of the calculation of the polynomials orthogonal on Sobolev, reducing it to use of well known recurrence relations for classical Meixner polynomials.

Key words: difference equation, Sobolev orthogonal polynomials, orthogonal on grid Meixner polynomials, discrete functions approximation, orthogonal on equidistant grid mixed series on Meixner polynomials.

Full text: PDF file (263 kB)
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UDC: 517.587
Received: 11.05.2016

Citation: I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Difference equations and Sobolev orthogonal polynomials, generated by Meixner polynomials”, Vladikavkaz. Mat. Zh., 19:2 (2017), 58–72

Citation in format AMSBIB
\Bibitem{ShaGadGad17}
\by I.~I.~Sharapudinov, Z.~D.~Gadzhieva, R.~M.~Gadzhimirzaev
\paper Difference equations and Sobolev orthogonal polynomials, generated by Meixner polynomials
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 2
\pages 58--72
\mathnet{http://mi.mathnet.ru/vmj617}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 29–39  mathnet  crossref
    2. M. S. Sultanakhmedov, “Cauchy problem for the difference equation and Sobolev orthogonal functions on the finite grid, generated by discrete orthogonal functions”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 77–85  mathnet  crossref
    3. R. M. Gadzhimirzaev, “Sobolev-orthonormal system of functions generated by the system of Laguerre functions”, Probl. anal. Issues Anal., 8(26):1 (2019), 32–46  mathnet  crossref
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