Author(s)

B. S. El-Desouky, F. A. Shiha, Ethar M. Shokr

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.

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.

Whitney Numbers, r-Whitney Numbers, p-Stirling Numbers, Generalized q-Stirling Numbers, Generalized Stirling Numbers

El-Desouky, B. , Shiha, F. and Shokr, E. (2017) The Generalized r-Whitney Numbers. Applied Mathematics, 8, 117-132. doi: 10.4236/am.2017.81010.