TITLE:
A Family of Generalized Stirling Numbers of the First Kind
AUTHORS:
Beih S. El-Desouky, Nabela A. El-Bedwehy, Abdelfattah Mustafa, Fatma M. Abdel Menem
KEYWORDS:
Stirling Numbers, Comtet Numbers, Creation, Annihilation, Differential Operator, Maple Program
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.10,
June
5,
2014
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.