A Unified Approach to Generalized Stirling Functions
Received:February 03, 2012  Revised:May 22, 2012
Key Word: Stirling numbers   Stirling functions   factorial polynomials   generalized factorial   divided difference   $k$-Gamma functions   Pochhammer symbol and $k$-Pochhammer symbol.  
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Author NameAffiliation
Tianxiao HE Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA 
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      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.
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