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Journal of Siberian Federal University. Mathematics & Physics, 2023, Volume 16, Issue 2, Pages 153–161 (Mi jsfu1065)  
Summation of functions and polynomial solutions to a multidimensional difference equation

Andrey A. Grigorieva, Evgeniy K. Leinartasa, Alexander P. Lyapinab

a Siberian Federal University, Krasnoyarsk, Russian Federation
b Fairmont State University, Fairmont, WV, USA
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Abstract: We define a set of polynomial difference operators which allows us to solve the summation problem and describe the space of polynomial solutions for these operators in equations with the polynomial right-hand side. The criterion describing these polynomial difference operators was obtained. The theorem describing the space of polynomial solutions for the operators was proved.
Keywords: Bernoulli numbers, Bernoulli polynomials, summation problem, multidimensional difference equation, Euler–Maclaurin formula, Todd operator.
Funding agency Grant number
Russian Science Foundation 20-11-20117
The second author is supported by the Russian Science Foundation no. 20-11-20117.
Received: 10.10.2022
Received in revised form: 09.11.2022
Accepted: 08.12.2022
Bibliographic databases:
Document Type: Article
UDC: 517.55
Language: English
Citation: Andrey A. Grigoriev, Evgeniy K. Leinartas, Alexander P. Lyapin, “Summation of functions and polynomial solutions to a multidimensional difference equation”, J. Sib. Fed. Univ. Math. Phys., 16:2 (2023), 153–161
Citation in format AMSBIB
\Bibitem{GriLeiLya23}
\by Andrey~A.~Grigoriev, Evgeniy~K.~Leinartas, Alexander~P.~Lyapin
\paper Summation of functions and polynomial solutions to a multidimensional difference equation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2023
\vol 16
\issue 2
\pages 153--161
\mathnet{http://mi.mathnet.ru/jsfu1065}
\edn{https://elibrary.ru/BBJNGZ}
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