Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials

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 Lip...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-01, Vol.14 (1), p.35
Main Authors: Corcino, Cristina B., Corcino, Roberto B., Damgo, Baby Ann A., Cañete, Joy Ann A.
Format: Article
Language:English
Subjects:
bernoulli polynomials
Computational mathematics
euler polynomials
Fourier series
generating functions
genocchi polynomials
Polynomials
Representations
Series expansion
tangent polynomials
Theorems
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14010035