Сибирский федеральный университет

Тип публикации: статья из журнала

Год издания: 2022

Идентификатор DOI: 10.33048/semi.2022.19.008

Ключевые слова: summation of functions, euler-maclaurin formula, borel transform of power series

Аннотация: 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. 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. © 2022, Siberian Electronic Mathematical Reports. All rights reserved.

Журнал: SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA

Выпуск журнала: Vol. 19, Is. 1

Номера страниц: 91-100

ISSN журнала: 18133304

Место издания: NOVOSIBIRSK

Издатель: SOBOLEV INST MATHEMATICS

• Leinartas E.K. (Siberian Fed Univ, 79 Svobodny Ave, Krasnoyarsk 660041, Russia)
• Petrochenko M.E. (Siberian Fed Univ, 79 Svobodny Ave, Krasnoyarsk 660041, Russia)

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