Riordan阵的差分性质及其应用

Difference Properties of Riordan Arrays and Their Applications

中文关键词:  Riordan阵  第一类和第二类Stirling数  第一类和第二类B型Stirling数  Gegenbauer-Humbert型多项式

英文关键词:Riordan array  stirling number  stirling number of type $B$  Gegenbauer-Humbert-type polynomial

中文摘要:

      本文考虑了Riordan阵的差分性质, 并给出一些涉及经典组合序列的差分恒等式, 包括广义Stirling数, 第一类和第二类Stirling数, 第一类和第二类B型Stirling数以及Gegenbauer-Humbert型多项式.

英文摘要:

      In this paper, we consider the difference properties of Riordan arrays. As their applications, we provide some difference identities involving several classical combinatorial sequences such as the generalized Stirling numbers, including Stirling numbers of the first and second kinds and Stirling numbers of type $B$ of the first and second kinds, and Gegenbauer-Humbert-type polynomials.