A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

Abstract

Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials ${\tilde{U}}_n(x)$. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials ${\tilde{U}}_n(x)$ in complex plane. We find out some identities and properties related to polynomials ${\tilde{U}}_n(x)$. Finally, we also derive interesting relations between polynomials ${\tilde{U}}_n(x)$, Stirling numbers, central factorial numbers, and Euler numbers.