Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c
Cristina B Corcino | Baby Ann A Damgo | Roberto B. Corcino | Joy Ann A Cañete
Discipline: Mathematics
Abstract:
This paper presents new approximation formulas for the tangent
polynomials and Apostol-tangent polynomials of complex order, specifically
for large values of n. These polynomials are parameterized by a,b, and c. The
derivation of these formulas is accomplished through contour integration
techniques, where the contour is carefully selected to avoid branch cuts
introduced by the presence of multiple singularities within the integration
path. The analysis includes a detailed computation of the singularities
associated with the generating functions used in this process, ensuring the
accuracy and rigor of the derived formulas. Additionally, the paper provides
corollary results that reinforce and affirm the newly established formulas,
offering a comprehensive understanding of the behavior of these polynomials
under specified conditions.
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