A discrete analog of Euler's summation formula

被引：5
|
作者：
Ustinov, AV [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Moscow 117234, Russia
来源：
MATHEMATICAL NOTES | 2002年 / 71卷 / 5-6期
基金：
俄罗斯基础研究基金会;
关键词：
Euler's summation formula; Bernoulli polynomials; Fourier series;
D O I：
10.1023/A:1015833231580
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：851 / 856
页数：6
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