Name
Title | ||
|---|---|---|
The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jat.2010.02.005 | Journal of Approximation Theory |
Keywords | Field | DocType |
mobius inversion,mobius function,fourier expansion,fourier analysis,rational argument,euler polynomial,bius inversion formula,bernoulli polynomial,asymptotic property,bernoulli number,analytic number theory,fourier series,number theory,bernoulli polynomials | Bernoulli polynomials,Multiplication theorem,Orthogonal polynomials,Classical orthogonal polynomials,Mathematical analysis,Bernoulli process,Euler–Maclaurin formula,Discrete orthogonal polynomials,Bernoulli scheme,Mathematics | Journal |
Volume | Issue | ISSN |
163 | 1 | 0021-9045 |
Citations | PageRank | References |
5 | 1.08 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Luis M. Navas | 1 | 9 | 3.39 |
| Francisco Ruiz | 2 | 301 | 29.12 |
| Juan L. Varona | 3 | 17 | 4.81 |