Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers

Bayad, A.; Chikhi, J.

doi:10.1090/S0025-5718-2013-02699-3

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.

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