Bernoulli polynomials in several variables and summation of monomials over lattice points of a rational parallelotope

zbMath1348.11021MaRDI QIDQ332341

Ol'ga Andreevna Shishkina

Publication date: 8 November 2016

Published in: Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika (Search for Journal in Brave)

Full work available at URL: http://isu.ru/journal/downloadArticle?article=_8c77b92dca0945128324512895afd55d&lang=rus

zbMATH Keywords

generating functionsBernoulli numbers and polynomialsrational parallelotopesummation of functions

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Bernoulli and Euler numbers and polynomials (11B68)

Related Items (2)

The Euler-Maclaurin Formula in the Problem of Summation over Lattice Points of a Simplex ⋮ The Discrete Analog of the Newton-Leibniz Formula in the Problem of Summation over Simplex Lattice Points

Cites Work

• Constant coefficient linear difference equations on the rational cones of the integer lattice
• The Euler-Maclaurin formula for rational parallelotope
• Sufficient conditions of algebraicity of generating functions of the solutions of multidimensional difference equations
• Solvability of the Cauchy problem for a polynomial difference operator and monomial bases for the quotients of a polynomial ring
• Lattice points in simple polytopes
• Residue formulae, vector partition functions and lattice points in rational polytopes
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