A Family of Generalized Stirling Numbers of the First Kind

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.

DOI: 10.4236/am.2014.510150                

Abstract

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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