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Sbornik: Mathematics, 2015, Volume 206, Issue 8, Pages 1087–1122
DOI: https://doi.org/10.1070/SM2015v206n08ABEH004490 (Mi sm8413) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

D. V. Gorbachev, V. I. Ivanov

Tula State University
English version PDF (638 kB) Citations (17) Russian version article
References:
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DOI: https://doi.org/10.1070/SM2015v206n08ABEH004490
Abstract: Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given.
Bibliography: 39 titles.
Keywords: Gauss and Markov quadrature formulae, entire function of exponential type, Sturm-Liouville problem, Jacobi transform, Jacobi functions and polynomials.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00045
Ministry of Education and Science of the Russian Federation 5414ГЗ
1.1333.2014К
Dynasty Foundation
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 13-01-00045), the Ministry of Education and Science of the Russian Federation (state contract nos. 5414ГЗ and~1.1333.2014K) and D. Zimin's "Dynasty" foundation.
Received: 31.07.2014 and 14.11.2014
Bibliographic databases:
Document Type: Article
UDC: 517.518.87
MSC: Primary 41A55; Secondary 30D15, 34B25
Language: English
Original paper language: Russian
Citation: D. V. Gorbachev, V. I. Ivanov, “Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type”, Sb. Math., 206:8 (2015), 1087–1122
Citation in format AMSBIB
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\yr 2015
\vol 206
\issue 8
\pages 1087--1122
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    • This publication is cited in the following 17 articles:
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