A Newton Interpolation Approach to Generalized Stirling Numbers

[摘要] We employ the generalized factorials to define a Stirling-type pair{s(n,k;α,β,r),S(n,k;α,β,r)}which unifies various Stirling-type numbers investigated by previous authors. We make use of the Newton interpolation and divideddifferences 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.

[学科分类] 应用数学