关于第三类退化的Poly-Cauchy多项式的组合恒等式

Some Identities on Degenerate Poly-Cauchy Polynomials of the Third Kind

摘要: 本文利用发生函数和Riordan阵研究了第三类退化的Poly-Cauchy多项式相关的恒等式。首先，运用发生函数方法给出第三类退化的Poly-Cauchy多项式的性质，从而得到了关于第三类退化的Poly-Cauchy多项式的一些组合恒等式。其次，应用Riordan阵法，建立了第三类退化的Poly-Cauchy多项式与两类Stirling数、Lab数、Bell数之间的一些关系式。

Abstract: In this paper, using generating functions and Riordan arrays, we establish some identities involving the degenerate Poly-Cauchy polynomials of the third kind. Using the generating functions, we explore some properties of the degenerate Poly-Cauchy polynomials of the third kind, and obtain some combinatorial identities involving the degenerate Poly-Cauchy polynomials of the third kind. In addition, using Riordan arrays, we give some interesting relations involving degenerate Poly-Cauchy polynomials of the third kind with the Stirling numbers of both kinds, the Lab numbers and the Bell numbers.