A Family of Generalized Stirling Numbers of the First Kind

• 作者: Abdelfattah Mustafa Beih S. El-Desouky Fatma M. Abdel Menem Nabela A. El-Bedwehy
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: STIRLING NUMBERS Comtet NUMBERS CREATION ANNIHILATION Differential OPERATOR MAPLE Program
• 年，卷（期）: 2014,（10）
• 页码范围: 1573-1585
• 页数: 13页
• 分类号: O1

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.