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

Authors

  • Cristina B. Corcino (1) Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City, Philippines; (2) Mathematics Department, Cebu Normal University, Cebu City, Philippines https://orcid.org/0000-0003-1634-9605
  • Baby Ann A. Damgo Department of Mathematics and Statistics, Cebu Technological University, Cebu City, Philippines https://orcid.org/0009-0007-1776-7493
  • Roberto B. Corcino (1) Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City, Philippines; (2) Mathematics Department, Cebu Normal University, Cebu City, Philippines https://orcid.org/0000-0003-1681-1804
  • Joy Ann A. Cañete Department of Mathematics, Visayas State University, Baybay City, Philippines https://orcid.org/0009-0001-9078-3074

DOI:

https://doi.org/10.32871/rmrj2412.02.06

Keywords:

Asymptotic approximation, tangent polynomials, Apostol-tangent polynomials

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.

References

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Published

2024-12-31

How to Cite

Corcino, C. B., Damgo, B. A. A., Corcino, R. B., & Cañete, J. A. A. . (2024). Approximations of Apostol-Tangent Polynomials of Complex Order with Parameters a, b, and c. Recoletos Multidisciplinary Research Journal, 12(2), 77–90. https://doi.org/10.32871/rmrj2412.02.06

Issue

Vol. 12 No. 2 (2024)

Section

Articles

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