Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


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Sharapudinov I. I., Guseinov I. G. Polynomials Orthogonal with Respect to Sobolev Type Inner Product Generated by Charlier Polynomials. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 2, pp. 196-205. DOI: 10.18500/1816-9791-2018-18-2-196-205, EDN: XQFNRR

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.05.2018
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Russian
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Article
UDC: 
517.587
EDN: 
XQFNRR

Polynomials Orthogonal with Respect to Sobolev Type Inner Product Generated by Charlier Polynomials

Autors: 
Sharapudinov Idris Idrisovich, Daghestan Scientific Centre of Russian Academy of Sciences
Guseinov Ibraghim G., Daghestan Scientific Centre of Russian Academy of Sciences
Abstract: 

The problem of constructing of the Sobolev orthogonal polynomials s α r,n(x) generated by Charlier polynomials s α n (x) is considered. It is shown that the system of polynomials s α r,n(x) generated by Charlier polynomials is complete in the space Wr lρ , consisted of the discrete functions, given on the grid Ω = {0, 1, . . .}. Wr lρ is a Hilbert space with the inner product hf, gi. An explicit formula in the form of s α r,k+r (x) = P k l=0 b r l x [l+r] , where x [m] = x(x − 1). . .(x − m + 1), is found. The connection between the polynomials s α r,n(x) and the classical Charlier polynomials s α n (x)in the form of s α r,k+r (x) = U r k · s α k+r (x) − rP−1 ν=0 V r k,νx [ν] ¸ , where for the numbers U r k , V r k,ν we found the explicit expressions, is established.

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Received: 
05.01.2018
Accepted: 
28.04.2018
Published: 
04.06.2018
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