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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2022_19_1_a28,
     author = {E. K. Leinartas and M. E. Petrochenko},
     title = {Multidimensional analogues of the {Euler-Maclaurin} summation formula and the {Borel} transform of power series},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {91--100},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a28/}
}
TY  - JOUR
AU  - E. K. Leinartas
AU  - M. E. Petrochenko
TI  - Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 91
EP  - 100
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a28/
LA  - ru
ID  - SEMR_2022_19_1_a28
ER  - 
%0 Journal Article
%A E. K. Leinartas
%A M. E. Petrochenko
%T Multidimensional analogues of the Euler-Maclaurin summation formula and the Borel transform of power series
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 91-100
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a28/
%G ru
%F SEMR_2022_19_1_a28
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/