This article is cited in 9 papers

A Discrete Analog of Euler's Summation Formula

A. V. Ustinov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, we prove a discrete analog of Euler's summation formula. The difference from the classical Euler formula is in that the derivatives are replaced by finite differences and the integrals by finite sums. Instead of Bernoulli numbers and Bernoulli polynomials, special numbers $P_n$ and special polynomials $P_n(x)$ introduced by Korobov in 1996 appear in the formula.

UDC: 511.217

Received: 13.03.2001
Revised: 26.11.2001

DOI: 10.4213/mzm397

 English version: Mathematical Notes, 2002, 71:6, 851–856

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