New Family of Whitney Numbers

B. S. El-Desouky, Nenad P. Cakić, F. A. Shiha

In this paper we give a new family of numbers, called $\bar{\alpha}$-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.