Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607677 | Journal of Approximation Theory | 2011 | 19 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Luis M. Navas, Francisco J. Ruiz, Juan L. Varona,