Expression and Computation of Generalized Stirling Numbers

Here presented is a unified expression of Stirling numbers and their generalizations by using generalized factorial 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, and Ahuja-Enneking are included as particular
cases of our generalization. Four algorithms for calculating the Stirling numbers and their generalizations based on our unified form are also given, which include two comprehensive algorithms using the characterization of Riordan arrays.