A Unified Approach to Generalized Stirling Functions  

作　　者：Tianxiao HE 

机构地区：[1]Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA

出　　处：《Journal of Mathematical Research with Applications》2012年第6期631-646,共16页数学研究及应用（英文版）

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.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. 

分 类 号：O157.1[理学—数学] TU378.04[理学—基础数学]