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

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

[学科分类] 应用数学