Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers

Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers

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 fo...

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Veröffentlicht in:Mathematics of computation 2013-04, Vol.82 (284), p.2327-2332
Hauptverfasser: Bayad, A., Chikhi, J.
Format: Artikel
Sprache:eng
Schlagworte:
Fourier series
Integers
Mathematical functions
Mathematical theorems
Mathematics
Number Theory
Numbers
Polynomials
Research article
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Zusammenfassung: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2013-02699-3