Journal of Applied Mathematics

A Newton Interpolation Approach to Generalized Stirling Numbers

Aimin Xu

Abstract

We employ the generalized factorials to define a Stirling-type pair $\{s(n,k;\mathbf{\alpha },\mathbf{\beta },r),S(n,k;\mathbf{\alpha },\mathbf{\beta },r)\}$ which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divided differences to obtain some basic properties of the generalized Stirling numbers including the recurrence relation, explicit expression, and generating function. The generalizations of the well-known Dobinski's formula are further investigated.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 351935, 17 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495048

Digital Object Identifier
doi:10.1155/2012/351935

Mathematical Reviews number (MathSciNet)
MR2880860

Zentralblatt MATH identifier
1235.65014

Citation

Xu, Aimin. A Newton Interpolation Approach to Generalized Stirling Numbers. J. Appl. Math. 2012 (2012), Article ID 351935, 17 pages. doi:10.1155/2012/351935. https://projecteuclid.org/euclid.jam/1355495048