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The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials
- Source :
-
Journal of Approximation Theory . Jan2011, Vol. 163 Issue 1, p22-40. 19p. - Publication Year :
- 2011
-
Abstract
- 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 Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Bernoulli numbers, and the Möbius function; this includes formulas for the Bernoulli polynomials at rational arguments. Finally, we show some asymptotic properties concerning the Bernoulli and Euler polynomials. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00219045
- Volume :
- 163
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Approximation Theory
- Publication Type :
- Academic Journal
- Accession number :
- 55488929
- Full Text :
- https://doi.org/10.1016/j.jat.2010.02.005