The Mobius inversion formula for Fourier series applied to Bernoulli and Euler polynomials

被引：14

作者：

Navas, Luis M. ^{[2
]}

Ruiz, Francisco J. ^{[3
]}

Varona, Juan L. ^{[1
]}

机构：

[1] Univ La Rioja, Dept Matemat & Computac, Logrono 26004, Spain

[2] Univ Salamanca, Dept Matemat, E-37008 Salamanca, Spain

[3] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

来源：

JOURNAL OF APPROXIMATION THEORY | 2011年 / 163卷 / 01期

关键词：

Bernoulli polynomials; Euler polynomials; Fourier series; Mobius transform; Inversion formula; Rational arguments; Asymptotic properties;

D O I：

10.1016/j.jat.2010.02.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago In general Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner In addition applying the technique of Mobius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials Bernoulli numbers and the Mobius function this includes formulas for the Bernoulli polynomials at rational arguments Finally we show some asymptotic properties concerning the Bernoulli and Euler polynomials (C) 2010 Elsevier Inc All rights reserved

引用

页码：22 / 40

页数：19

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