Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers
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- by A. Bayad and J. Chikhi PDF
- Math. Comp. 82 (2013), 2327-2332 Request permission
Abstract:
In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit formulae for Apostol-Bernoulli numbers. These formulae involve Stirling numbers of the second kind and powers of cotangent. Our proofs are very simple.References
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Additional Information
- A. Bayad
- Affiliation: Département de mathématiques, Université d’Evry Val d’Essonne, Bâtiment I.B.G.B.I., 3ème étage, 23 Bd. de France, 91037 Evry Cedex, France
- Email: abayad@maths.univ-evry.fr
- J. Chikhi
- Affiliation: Département de mathématiques, Université d’Evry Val d’Essonne, Bâtiment I.B.G.B.I., 3ème étage, 23 Bd. de France, 91037 Evry Cedex, France
- Email: jchikhi@univ-evry.fr
- Received by editor(s): November 20, 2021
- Received by editor(s) in revised form: January 25, 2012
- Published electronically: April 24, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 82 (2013), 2327-2332
- MSC (2010): Primary 11B68, 11A25, 11B73, 42A16, 41A58
- DOI: https://doi.org/10.1090/S0025-5718-2013-02699-3
- MathSciNet review: 3073203