Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials

Luo, Qiu-Ming

doi:10.1090/S0025-5718-09-02230-3

Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
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by Qiu-Ming Luo;

Math. Comp. 78 (2009), 2193-2208

DOI: https://doi.org/10.1090/S0025-5718-09-02230-3

Published electronically: June 12, 2009

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Abstract:

We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit formulas at rational arguments for these polynomials in terms of the Hurwitz zeta function. We also derive the integral representations for the classical Bernoulli and Euler polynomials and related known results.

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