Asymptotic Approximation of the Apostol-Tangent Polynomials Using Fourier Series

Asymptotic approximations of the Apostol-tangent numbers and polynomials were established for non-zero complex values of the parameter λ. Fourier expansion of the Apostol-tangent polynomials was used to obtain the asymptotic approximations. The asymptotic formulas for the cases λ=1 and λ=−1 were exp...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-01, Vol.14 (1), p.53
Main Authors: Corcino, Cristina B., Damgo, Baby Ann A., Cañete, Joy Ann A., Corcino, Roberto B.
Format: Article
Language:English
Subjects:
Approximation
asymptotic approximation
Asymptotic properties
Asymptotic series
Bernoulli polynomials
Euler polynomials
Fourier series
generating functions
Genocchi polynomials
Numbers
Polynomials
tangent polynomials
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Summary:Asymptotic approximations of the Apostol-tangent numbers and polynomials were established for non-zero complex values of the parameter λ. Fourier expansion of the Apostol-tangent polynomials was used to obtain the asymptotic approximations. The asymptotic formulas for the cases λ=1 and λ=−1 were explicitly considered to obtain asymptotic approximations of the corresponding tangent numbers and polynomials.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14010053