Abstract:
In the problem of summation over lattice points of a simplex we find an analog of the Euler–Maclaurin formula for discrete primitive function and the sum.
Keywords:
summation of functions, a discrete primitive function, the Euler–Maclaurin formula.
The research of the first author is supported by the Krasnoyarsk Mathematical Center and
financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers of Mathematics Research and
Education (Agreement no. 075-02-2021-1388).
The research of the second athor was funded by RFBR, Krasnoyarsk Territory and Krasnoyarsk Regional Fund of Science, project number 20-41-243002.
Received: 29.07.2021 Received in revised form: 09.08.2021 Accepted: 15.09.2021
Bibliographic databases:
Document Type:
Article
UDC:517.55+517.962.26
Language: English
Citation:
Evgeniy K. Leinartas, Olga A. Shishkina, “The Euler–Maclaurin formula in the problem of summation over lattice points of a simplex”, J. Sib. Fed. Univ. Math. Phys., 15:1 (2022), 108–113
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\by Evgeniy~K.~Leinartas, Olga~A.~Shishkina
\paper The Euler--Maclaurin formula in the problem of summation over lattice points of a simplex
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2022
\vol 15
\issue 1
\pages 108--113
\mathnet{http://mi.mathnet.ru/jsfu980}
\crossref{https://doi.org/10.17516/1997-1397-2022-15-1-108-113}
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Linking options:
https://www.mathnet.ru/eng/jsfu980
https://www.mathnet.ru/eng/jsfu/v15/i1/p108
This publication is cited in the following 3 articles:
Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli, “Umbral Interpolation: A Survey”, Mathematics, 13:2 (2025), 271
Nianliang Wang, Takako Kuzumaki, Shigeru Kanemitsu, “A Tapestry of Ideas with Ramanujan's Formula Woven In”, Axioms, 14:2 (2025), 146
Yasir A. Madani, Abdulghani Muhyi, Khaled Aldwoah, Amel Touati, Khidir Shaib Mohamed, Ria H. Egami, “Construction of a Hybrid Class of Special Polynomials: Fubini–Bell-Based Appell Polynomials and Their Properties”, Mathematics, 13:6 (2025), 1009
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