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A modified approach via differential operator is given to derive a newfamily of generalized Stirling numbers of the first kind. This approach givesus an extension of the techniques given by El-Desouky 1 and Gould 2. Some new combinatorial identities and manyrelations between different types of Stirling numbers are found. Furthermore,some interesting special cases of the generalized Stirling numbers of the firstkind are deduced. Also, a connection between these numbers and the generalizedharmonic numbers is derived. Finally, some applications in coherent states andmatrix representation of some results obtained are given.

KEYWORDS

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

Cite this paper

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.





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

Source: http://www.scirp.org/



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