A Family of Generalized Stirling Numbers of the First Kind

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

作者机构：Mathematics Department Faculty of Science Damietta University Damietta Egypt Mathematics Department Faculty of Science Mansoura University Mansoura Egypt 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2014年第5卷第10期

页      面：1573-1585页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Stirling Numbers Comtet Numbers Creation Annihilation Differential Operator Maple Program 

摘      要：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.