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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 1, Pages 91–100
DOI: https://doi.org/10.33048/semi.2022.19.008 (Mi semr1483) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Real, complex and functional analysis

Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series

E. K. Leinartas, M. E. Petrochenko

Siberian Federal University, 79, Svobodny ave., Krasnoyarsk, 660041, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.008
Abstract: The aim of the paper is to study the problem of summation of functions of a discrete variable on integer points in a rational parallelepiped. Our method is based on Borel’s transform of power series. Integral representation for discrete antiderivative and a new variant of the Euler-Maclaurin formula are described. Consequently new identities satisfied by Bernoulli’s polynomials are obtained.
Keywords: summation of functions, Euler-Maclaurin formula, Borel transform of power series.
Funding agency Grant number
Russian Science Foundation 20-11-20117
Received December 7, 2020, published January 24, 2022
Bibliographic databases:
Document Type: Article
UDC: 517.962.1, 517.55
MSC: 65B15, 32A15
Language: Russian
Citation: E. K. Leinartas, M. E. Petrochenko, “Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series”, Sib. Èlektron. Mat. Izv., 19:1 (2022), 91–100
Citation in format AMSBIB
\Bibitem{LeiPet22}
\by E.~K.~Leinartas, M.~E.~Petrochenko
\paper Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 1
\pages 91--100
\mathnet{http://mi.mathnet.ru/semr1483}
\crossref{https://doi.org/10.33048/semi.2022.19.008}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4377436}
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  • https://www.mathnet.ru/eng/semr/v19/i1/p91
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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