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Fourier expansions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

Author: A. Bayad
Journal: Math. Comp. 80 (2011), 2219-2221
MSC (2010): Primary 11Yxx, 30D30
Published electronically: March 7, 2011
MathSciNet review: 2813356
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Abstract: We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

References [Enhancements On Off] (What's this?)

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  • 2. R. Lipschitz, Untersuchung der Eigenschaften einer Gattung von unendlichen Reihen, J. Reine und Angew. Math. CV (1889), 127-156.
  • 3. H. Liu, W. Wang, Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums, Discrete Math., Volume 309, 10, (2009), 3346-3363. MR 2526753 (2010i:11031)
  • 4. Q-M. Luo, Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials, Math. Comp., Volume 78 (2009), No. 268, 2193-2208. MR 2521285 (2010d:11029)

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Additional Information

A. Bayad
Affiliation: Département de Mathématiques, Université d’Évry Val d’Essonne, Bd. F. Mitterrand, 91025 Évry Cedex, France

Keywords: Fourier series, Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi numbers and polynomials, residue theorem
Received by editor(s): July 19, 2010
Received by editor(s) in revised form: August 14, 2010
Published electronically: March 7, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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