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Daghestan Electronic Mathematical Reports, 2016, Issue 6, Pages 1–24 (Mi demr26)  

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

Asymptotic properties of polynomials, orthogonal in Sobolev sence and associated with the Jacobi polynomials

I. I. Sharapudinovab

a Daghestan Scientific Centre of RAS
b Daghestan State Pedagogical University

Abstract: We consider polynomials $p_{r,n}^{\alpha,\beta}(x)$ $(n=0,1,\ldots)$, generated by classical Jacobi polynomials $p_{n}^{\alpha,\beta}(x)$ and forming orthonormal system with respect to Sobolev-type inner product
\begin{equation*} <f,g>=\sum_{\nu=0}^{r-1}f^{(\nu)}(-1)g^{(\nu)}(-1)+\int_{-1}^{1}f^{(r)}(t)g^{(r)}(t)\rho(t) dt, \end{equation*}
where $\rho(x)=(1-x)^\alpha(1+x)^\beta$ – Jacobi weight function. The explicit \linebreak representations for polynomials $p_{r,n}^{\alpha,\beta}(x)$ are obtained and using these ones the asymptotic properties of polynomials $p_{r,n}^{\alpha,\beta}(x)$ are investigated.

Keywords: orthogonal polynomials, Sobolev orthogonal polynomials, Jacobi polynomials, Chebyshev polynomials of the first kind, Legendre polynomials

DOI: https://doi.org/10.31029/demr.6.1

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Full text: http://mathreports.ru/.../asimptotichescheskie-svoystva-polinomov-ortogonalnykh-po-sobolevu-porozhdennykh-polinomami-yakobi
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UDC: 517.538
Received: 27.06.2016
Revised: 09.08.2016
Accepted:10.08.2016

Citation: I. I. Sharapudinov, “Asymptotic properties of polynomials, orthogonal in Sobolev sence and associated with the Jacobi polynomials”, Daghestan Electronic Mathematical Reports, 2016, no. 6, 1–24

Citation in format AMSBIB
\Bibitem{Sha16}
\by I.~I.~Sharapudinov
\paper Asymptotic properties of polynomials, orthogonal in Sobolev sence and associated with the Jacobi polynomials
\jour Daghestan Electronic Mathematical Reports
\yr 2016
\issue 6
\pages 1--24
\mathnet{http://mi.mathnet.ru/demr26}
\crossref{https://doi.org/10.31029/demr.6.1}
\elib{http://elibrary.ru/item.asp?id=https://elibrary.ru/item.asp?id=29409283}


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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, “O priblizhenii resheniya zadachi Koshi dlya nelineinykh sistem ODU posredstvom ryadov Fure po funktsiyam, ortogonalnym po Sobolevu”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 66–76  mathnet  crossref
    2. I. I. Sharapudinov, M. G. Magomed-Kasumov, “Chislennyi metod resheniya zadachi Koshi dlya sistem obyknovennykh differentsialnykh uravnenii s pomoschyu ortogonalnoi v smysle Soboleva sistemy, porozhdennoi sistemoi kosinusov”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 53–60  mathnet  crossref
    3. I. I. Sharapudinov, “Sobolev-orthogonal systems of functions and the Cauchy problem for ODEs”, Izv. Math., 83:2 (2019), 391–412  mathnet  crossref  crossref  adsnasa  isi  elib
  • Daghestan Electronic Mathematical Reports
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