A family of two-variable derivative polynomials for tangent and secant

TL;DR

This paper introduces a new family of two-variable derivative polynomials for tangent and secant functions, explores their generating functions, and links them to Eulerian polynomials, enriching the mathematical understanding of these functions.

Contribution

It presents a novel family of derivative polynomials for tangent and secant, along with their generating functions and connections to Eulerian polynomials.

Findings

Derived explicit generating functions for the polynomial family

Established a connection between these polynomials and Eulerian polynomials

Provided new insights into the structure of tangent and secant derivatives

Abstract

In this paper we introduce a family of two-variable derivative polynomials for tangent and secant. We study the generating functions for the coefficients of this family of polynomials. In particular, we establish a connection between these generating functions and Eulerian polynomials.