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Asymptotic Approximation of the Apostol-Tangent Polynomials Using Fourier Series

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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… Click to show full abstract

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.

Keywords: asymptotic approximation; asymptotic approximations; apostol tangent; tangent polynomials

Journal Title: Symmetry
Year Published: 2022

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