Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
Open Access
- 12 June 2009
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 78 (268) , 2193-2208
- https://doi.org/10.1090/s0025-5718-09-02230-3
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.Keywords
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