Publication Date
October 2012
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 \cite{He11}. Previous well-known Stirling functions introduced by Butzer and Hauss \cite{BH93}, Butzer, Kilbas, and Trujilloet \cite{BKT03} 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 \cite{HS98} to the defined Stirling functions.
Disciplines
Applied Mathematics | Mathematics
Recommended Citation
He, Tian-Xiao, "A Unified Approach to Generalized Stirling Functions" (2012). Scholarship. 37.
https://digitalcommons.iwu.edu/math_scholarship/37