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A Unified Approach to Generalized Stirling Functions
作者姓名:Tianxiao  HE
作者单位:Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA
摘    要:Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, k-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in 16]. Previous well-known Stirling functions introduced by Butzer and Hauss 4], Butzer, Kilbas, and Trujilloet 6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed,which extend the corresponding results about the Stirling numbers shown in 21] to the defined Stirling functions.

关 键 词:Stirling  numbers  Stirling  functions  factorial  polynomials  generalized  factorial  divided  difference  k-Gamma  functions  Pochhammer  symbol  and  k-Pochhammer  symbol.
收稿时间:2/3/2012 12:00:00 AM
修稿时间:2012/5/22 0:00:00

A Unified Approach to Generalized Stirling Functions
Tianxiao HE.A Unified Approach to Generalized Stirling Functions[J].Journal of Mathematical Research with Applications,2012,32(6):631-640.
Authors:Tianxiao HE
Institution:Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA
Abstract:Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in 16]. Previous well-known Stirling functions introduced by Butzer and Hauss 4], Butzer, Kilbas, and Trujilloet 6] and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in 21] to the defined Stirling functions.
Keywords:Stirling numbers  Stirling functions  factorial  polynomials  generalized factorial  divided difference  $k$-Gamma functions  Pochhammer symbol and $k$-Pochhammer symbol  
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