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Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials. (English) Zbl 1214.11032
The Lipschitz summation formula is used to obtain Fourier expansions and integral representations of the polynomials in the title. Explicit formulas at rational arguments for these polynomials are given in terms of the Hurwitz zeta function. Integral representations for the classical Bernoulli and Euler polynomials are also described.

##### MSC:
 11B68 Bernoulli and Euler numbers and polynomials 11M35 Hurwitz and Lerch zeta functions 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
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##### References:
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