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

DOI10.1016/j.jat.2010.02.005zbMath1253.11028OpenAlexW2051938226MaRDI QIDQ619073

Luis M. Navas, Francisco J. Ruiz, Juan Luis Varona

Publication date: 21 January 2011

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2010.02.005

zbMATH Keywords

asymptotic propertiesinversion formulaFourier seriesBernoulli polynomialsMöbius transformEuler polynomialsrational arguments

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Arithmetic functions; related numbers; inversion formulas (11A25) Matrices, determinants in number theory (11C20)

Related Items (16)

Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials ⋮ A note on Appell sequences, Mellin transforms and Fourier series ⋮ A class of subsums of Euler's sum ⋮ Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers ⋮ Asymptotic behavior of the Lerch transcendent function ⋮ Beyond the Basel Problem, Part I ⋮ Results on values of Barnes polynomials ⋮ On Ramanujan expansions with multiplicative coefficients ⋮ On a generalization of a theorem by Euler ⋮ Old and new identities for Bernoulli polynomials via Fourier series ⋮ Möbius inversion formulas related to the Fourier expansions of two-dimensional Apostol-Bernoulli polynomials ⋮ Asymptotic behavior of Bernoulli-Dunkl and Euler-Dunkl polynomials and their zeros ⋮ Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function ⋮ A method for summing Bessel series and a couple of illustrative examples ⋮ The Lerch transcendent from the point of view of Fourier analysis ⋮ Identities for Dirichlet and Lambert-type series arising from the numbers of a certain special word

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A transform involving Chebyshev polynomials and its inversion formula
• Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials
• Two problems related to the non-vanishing of \(L(1,\chi)\)
• Möbius inversion formulas for flows of arithmetic semigroups
• Evaluation of Dirichlet Series
• Some formulas for the Bernoulli and Euler polynomials at rational arguments
• New Formulae for the Bernoulli and Euler Polynomials at Rational Arguments
• The Möbius inversion and Fourier coefficients.

This page was built for publication: The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials