Asymptotic approximations of complex order tangent, Tangent-Bernoulli and Tangent-Genocchi polynomials

Abstract

In this study, asymptotic formulas for complex order Tangent, Tangent-Bernoulli, and Tangent-Genocchi polynomials are obtained through the method of contour integration, strategically avoiding branch cuts in the process. By employing this technique, the paper elucidates the behavior of these polynomials in the complex plane. Additionally, the investigation expands upon the Taylor series expansion of these functions, revealing alternative asymptotic expansions. This dual approach not only enhances our understanding of the asymptotic properties of these polynomials but also offers alternative mathematical perspectives, enriching the existing body of knowledge in this field.

Keywords:

• Asymptotic approximation
• Bernoulli polynomials
• Euler polynomials
• Genocchi polynomials
• Tangent-Bernoulli polynomials and Tangent-Genocchi polynomials
• tangent polynomials

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors would like to thank Cebu Normal University (CNU) for funding this research project through its Research Institute for Computational Mathematics and Physics (RICMP).