Geodesic
Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 91-100.

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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. 
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E. K. Leinartas; M. E. Petrochenko. Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 91-100. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a28/

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