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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
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.
Received December 7, 2020, published January 24, 2022
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
Linking options:
https://www.mathnet.ru/eng/semr1483 https://www.mathnet.ru/eng/semr/v19/i1/p91
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Abstract page: | 135 | Full-text PDF : | 61 | References: | 14 |
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