Asymptotics of Riemann Sums for Uniform Partitions of Intervals of Integration

被引：0

作者：

Adam, Marcin ^{[1
]}

Ludew, Jakub Jan ^{[1
]}

Rozanski, Michal ^{[1
]}

Smuda, Adrian ^{[1
]}

Witula, Roman ^{[1
]}

机构：

[1] Silesian Tech Univ, Dept Math, Kaszubska 23, PL-44100 Gliwice, Poland

来源：

SYMMETRY-BASEL | 2025年 / 17卷 / 02期

关键词：

uniform Riemann sums; asymptotic of uniform Riemann sums; Euler-Maclaurin summation formula; Lagrange's mean value theorem; Taylor formula with the Lagrange form of the remainder; Bernstein operators; APPROXIMATION; OPERATORS;

D O I：

10.3390/sym17020226

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Our goal is to prove the Euler-Maclaurin summation formula using only the Taylor formula. Furthermore, the Euler-Maclaurin summation formula will be considered for the case of functions of the class C2k([a,b]). A stronger version of the estimation of the rest for functions of class Cn([a,b]) is given. We will also present the application of the obtained Euler-Maclaurin summation formulas to determine the asymptotics of Riemann sums for uniform partitions of intervals of integration. This paper also introduces the concepts of the asymptotic smoothing of the graph of a given function, as well as the asymptotic uniform distribution of the positive and negative values of the given function (generalizing the concept of the symmetric distribution of these values with respect to the x-axis, as in the case of the Peano-Jordan measure).

引用

页数：17

共 33 条

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