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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 5, Pages 201–224 (Mi izv8117)  

This article is cited in 6 scientific papers (total in 6 papers)

Some special series in ultraspherical polynomials and their approximation properties

I. I. Sharapudinov

Daghestan Scientific Centre of the Russian Academy of Sciences, Makhachkala

Abstract: Using the explicit form of a limiting ultraspherical series $\sum_{k=0}^\infty f_k^{-1}\widehat P_k^{-1}(x)$, which was established by us in [1], we consider new, more general, special series in ultraspherical Jacobi polynomials and their approximation properties. We show that as an approximation tool, these series compare favourably with Fourier series in Jacobi polynomials. At the same time, they admit a simple construction, which in important particular cases enables one to use the fast Fourier transform for the numerical realization of their partial sums.

Keywords: Jacobi polynomial, special series in ultraspherical polynomials, approximation by partial sums of special series.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00191


DOI: https://doi.org/10.4213/im8117

Full text: PDF file (602 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2014, 78:5, 1036–1059

Bibliographic databases:

UDC: 517.538
MSC: 33C45, 41A58, 42C10
Received: 20.03.2013
Revised: 24.06.2013

Citation: I. I. Sharapudinov, “Some special series in ultraspherical polynomials and their approximation properties”, Izv. RAN. Ser. Mat., 78:5 (2014), 201–224; Izv. Math., 78:5 (2014), 1036–1059

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. I. Sharapudinov, “Nekotorye spetsialnye dvumernye ryady po sisteme $\{\sin x\sin kx\}$ i ikh approksimativnye svoistva”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(1) (2014), 407–412  mathnet  crossref  elib
    2. I. I. Sharapudinov, G. G. Akniev, “Diskretnye preobrazovaniya so svoistvom prilipaniya na osnove sistemy $\{\sin x\sin kx\}$ i sistemy polinomov Chebysheva vtorogo roda”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(1) (2014), 413–422  mathnet  crossref  elib
    3. I. I. Sharapudinov, “Approximation properties of Fejér- and de la Valleé-Poussin-type means for partial sums of a special series in the system $\{\sin x\sin kx\}_{k=1}^\infty$”, Sb. Math., 206:4 (2015), 600–617  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. M. S. Sultanakhmedov, “Spetsialnye veivlety na osnove polinomov Chebysheva vtorogo roda”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:1 (2016), 34–41  mathnet  crossref  mathscinet  elib
    5. I. I. Sharapudinov, “Sobolev orthogonal polynomials generated by Jacobi and Legendre polynomials, and special series with the sticking property for their partial sums”, Sb. Math., 209:9 (2018), 1390–1417  mathnet  crossref  crossref  adsnasa  isi  elib
    6. I. I. Sharapudinov, “Sobolev-orthogonal systems of functions and some of their applications”, Russian Math. Surveys, 74:4 (2019), 659–733  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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