Author(s)

Beih S. El-Desouky, Nabela A. El-Bedwehy, Abdelfattah Mustafa, Fatma M. Abdel Menem

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

A modified approach via differential operator is given to derive a new family of generalized Stirling numbers of the first kind. This approach gives us an extension of the techniques given by El-Desouky [1] and Gould [2]. Some new combinatorial identities and many relations between different types of Stirling numbers are found. Furthermore, some interesting special cases of the generalized Stirling numbers of the first kind are deduced. Also, a connection between these numbers and the generalized harmonic numbers is derived. Finally, some applications in coherent states and matrix representation of some results obtained are given.

Stirling Numbers, Comtet Numbers, Creation, Annihilation, Differential Operator, Maple Program

El-Desouky, B. , El-Bedwehy, N. , Mustafa, A. and Menem, F. (2014) A Family of Generalized Stirling Numbers of the First Kind. Applied Mathematics, 5, 1573-1585. doi: 10.4236/am.2014.510150.