Further Results for Hermite-Based Milne-Thomson Type Fubini Polynomials with Trigonometric Functions

Abstract

This paper examines generating functions of r-parametric Hermite-based Milne-Thomson polynomials. Using generating function methods, the relationships among these polynomials, Fubini type polynomials, and trigonometric functions are given. Moreover, new formulas are derived by utilizing not only the generating functions of these polynomials but also associated functional equations. These formulas pertain to r-parametric Hermite-based sine-and cosine-Milne-Thomson Fubini polynomials, as well as Stirling type polynomials and numbers. Additionally, by analyzing special cases of newly obtained results, some known formulas are also derived. Furthermore, some identities involving secant and cosecant numbers are derived through the properties of trigonometric functions. Special polynomials and their generating functions are an important tool for solving some problems in many areas such as combinatorics and number theory. By introducing new formulas, this paper significantly enhances these problems-solving abilities in these areas. Consequently, these results have potential to shed light on important applications in mathematics, engineering, and mathematical physics.