Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c

Roberto  B. Corcino,; Cristina  B. Corcino,; Baby Ann  A. Damgo,; Joy Ann  A. Cañete,

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

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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