Geodesic
Summation of functions and polynomial solutions to a multidimensional difference equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 2, pp. 153-161

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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, summation problem, multidimensional difference equation, Euler–Maclaurin formula, Todd operator.
Mots-clés : Bernoulli polynomials 
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Andrey A. Grigoriev; Evgeniy K. Leinartas; Alexander P. Lyapin. Summation of functions and polynomial solutions to a multidimensional difference equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 2, pp. 153-161. http://geodesic.mathdoc.fr/item/JSFU_2023_16_2_a0/