The Euler-Maclaurin Formula and Differential Operators of Infinite Order

Abstract

We use methods of the theory of differential operators of infinite order for solving difference equations and for generalizing the Euler-Maclaurin formula in the case of multiple summation.

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

“…Let us note that the case φ (t) = ψ (∥t∥), where ψ (τ ) is a function of one variable was considered [10].…”

“…Summation of arbitrary functions over integer points of a rational parallelotop was studied [8][9][10]. Euler approach based on definitions of discrete primitive function and discrete analog of the Newton-Leibniz formula was used to solve the problem.…”