  Here presented is a unified approach to Stirling numbers and their
generalizations as well as generalized Stirling functions by using generalized
factorial functions, $k$-Gamma functions, and generalized divided difference.
Previous well-known extensions of Stirling numbers due to Riordan, Carlitz,
Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov,
Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer,
Kilbas, and Trujilloet and others are included as particular cases of our
generalization. Some basic properties related to our general pattern such as
their recursive relations and generating functions are discussed. Three
algorithms for calculating the Stirling numbers based on our generalization are
also given, which include a comprehensive algorithm using the characterization
of Riordan arrays.
