Riordan阵与广义λ-Array Type多项式恒等式
Generalized λ-Array Type Polynomials with Exponential Riordan Array

DOI: 10.12677/PM.2016.63043, PP. 288-298

Keywords: 指数型Riordan阵，广义λ-Array Type多项式，经典Array Type多项式，第二类Stirling数
Exponential Riordan Array, Generalized λ-Array Type Polynomials, Classical Array Type Polynomials, Stirling Numbers of the Second Kind

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Abstract:

在本文中定义了一类广义λ-array多项式，并利用运用指数型Riordan阵方法与组合分析法，研究了广义λ-array type多项式，得到了广义λ-array type多项式与广义Hermite-Based Apostol Bernoulli多项式，广义Hermite-Based Apostol Euler多项式的关系式，给出了array type多项式，第二类Stirling数以及高阶Bernoulli多项式，高阶Euler多项式的一些恒等式。
In this paper, by using exponential Riordan array methods, we proved some identities among the generalized λ-array type polynomials, the generalized Hermite-Based Apostol Bernoulli polyno-mials and the generalized Hermite-Based Apostol Euler polynomials. We also obtain some combi-natorial identities involving the classical array type polynomials, the Stirling number of the second kind, the generalized Bernoulli polynomials and the generalized Euler polynomials.

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