TITLE:
The Generalized r-Whitney Numbers
AUTHORS:
B. S. El-Desouky, F. A. Shiha, Ethar M. Shokr
KEYWORDS:
Whitney Numbers, r-Whitney Numbers, p-Stirling Numbers, Generalized q-Stirling Numbers, Generalized Stirling Numbers
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.1,
January
26,
2017
ABSTRACT: In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.