多元Stirling数及其性质

Multivariate Stirling Numbers and Their Properties

本文借用s元的Kergin插值理论以及插值公式定义了一类多元广义Stirling数偶S_1(α,β),S_2(α,β),作为古典Stirling数偶的一种推广。并研究了S_1(α,β),S_2(α,β)的一些性质,如正交性、递推关系、反演公式等。

A kind of muttivariate generalized stirling number pairs is defined in this paper by using s-variate Kergin interpolation and interpolatory formula. The s-variate Stirling number pairs, S_1 (α, β) and S_2 (α,β), extend the classical Stirling number pair in univariate case to multivariate case. Some properties of S_1 (α, β) and S_2(α, β)are also studied, such as orthogonality, recurrent relations and reciprocal formulae.