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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, Volume 18, Issue 2, Pages 196–205
DOI: https://doi.org/10.18500/1816-9791-2018-18-2-196-205
(Mi isu755)
 

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

Scientific Part
Mathematics

Polynomials orthogonal with respect to Sobolev type inner product generated by Charlier polynomials

I. I. Sharapudinova, I. G. Guseinovba

a Dagestan Scientific Center of RAS, 45, M. Gadzhieva Str., Makhachkala, 367025, Russia
b Dagestan State University, 43-a, M. Gadzhieva Str., Makhachkala, 367000, Russia
Full-text PDF (182 kB) Citations (3)
References:
Abstract: The problem of constructing of the Sobolev orthogonal polynomials $s_{r,n}^\alpha(x)$ generated by Charlier polynomials $s_n^\alpha(x)$ is considered. It is shown that the system of polynomials $s_{r,n}^\alpha(x)$ generated by Charlier polynomials is complete in the space $W^r_{l_\rho}$, consisted of the discrete functions, given on the grid $\Omega=\{0,1,\ldots\}$. $W^r_{l_\rho}$ is a Hilbert space with the inner product $\langle f,g \rangle$. An explicit formula in the form of $s_{r,k+r}^{\alpha}(x) = \sum\limits_{l=0}^{k} b_l^r x^{[l+r]} $, where $x^{[m]} = x(x-1)\ldots(x-m+1)$, is found. The connection between the polynomials $s_{r,n}^\alpha(x)$ and the classical Charlier polynomials $s_n^\alpha(x)$ in the form of $s_{r,k+r}^{\alpha}(x)= U_k^r \left[s_{k+r}^{\alpha}(x) - \sum\limits_{\nu=0}^{r-1} V_{k,\nu}^r x^{[\nu]}\right]$, where for the numbers $U_k^r$, $V_{k,\nu}^r$ we found the explicit expressions, is established.
Key words: Sobolev orthogonal polynomials, Charlier polynomials, Sobolev-type inner product.
Bibliographic databases:
Document Type: Article
UDC: 517.587
Language: Russian
Citation: I. I. Sharapudinov, I. G. Guseinov, “Polynomials orthogonal with respect to Sobolev type inner product generated by Charlier polynomials”, Izv. Saratov Univ. Math. Mech. Inform., 18:2 (2018), 196–205
Citation in format AMSBIB
\Bibitem{ShaGus18}
\by I.~I.~Sharapudinov, I.~G.~Guseinov
\paper Polynomials orthogonal with respect to Sobolev type inner product generated by Charlier polynomials
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2018
\vol 18
\issue 2
\pages 196--205
\mathnet{http://mi.mathnet.ru/isu755}
\crossref{https://doi.org/10.18500/1816-9791-2018-18-2-196-205}
\elib{https://elibrary.ru/item.asp?id=35085049}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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