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
收藏
页码：22 / 40
页数：19
相关论文
共 50 条
  • [1] Mobius inversion formulas related to the Fourier expansions of two-dimensional Apostol-Bernoulli polynomials
    Bayad, Abdelmejid
    Navas, Luis
    [J]. JOURNAL OF NUMBER THEORY, 2016, 163 : 457 - 473
  • [2] Proof of a conjectured Mobius inversion formula for Grothendieck polynomials
    Pechenik, Oliver
    Satriano, Matthew
    [J]. SELECTA MATHEMATICA-NEW SERIES, 2024, 30 (05):
  • [3] Euler polynomials, Bernoulli polynomials, and Levy's stochastic area formula
    Ikeda, Nobuyuki
    Taniguchi, Setsuo
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2011, 135 (6-7): : 684 - 694
  • [4] Fractional Fourier Analysis Using the Mobius Inversion Formula
    Miao, Hongxia
    Zhang, Feng
    Tao, Ran
    [J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2019, 67 (12) : 3181 - 3196
  • [5] Fourier Series of the Periodic Bernoulli and Euler Functions
    Ryoo, Cheon Seoung
    Kwon, Hyuck In
    Yoon, Jihee
    Jang, Yu Seon
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [6] MOBIUS INVERSION FORMULAE FOR APOSTOL-BERNOULLI TYPE POLYNOMIALS AND NUMBERS
    Bayad, A.
    Chikhi, J.
    [J]. MATHEMATICS OF COMPUTATION, 2013, 82 (284) : 2327 - 2332
  • [7] A New Formula of Products of the Apostol–Bernoulli and Apostol–Euler Polynomials
    Yuan He
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39 : 1307 - 1318
  • [8] Fourier Series for Bernoulli-Type Polynomials, Euler-Type Polynomials and Genocchi-Type Polynomials of Integer Order
    Corcino, Cristina B.
    Corcino, Roberto B.
    [J]. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, 15 (04): : 1662 - 1682
  • [9] Computing coefficients of wavelet series by Mobius inversion formula
    Chen, ZD
    Chen, NX
    [J]. PROGRESS IN NATURAL SCIENCE, 1997, 7 (02): : 163 - 171
  • [10] ON EULER AND BERNOULLI POLYNOMIALS
    BRILLHAR.J
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1969, 234 : 45 - &
12345