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Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials
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The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula at rational arguments of these polynomials. Using the Lipschitz summation formula, an integral representation of Apostol–tangent polynomials is also obtained.
Title: Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials
Description:
The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour.
This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula at rational arguments of these polynomials.
Using the Lipschitz summation formula, an integral representation of Apostol–tangent polynomials is also obtained.
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