理论数学  >> Vol. 6 No. 3 (May 2016)

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, PDF, HTML, XML, 下载: 1,403  浏览: 4,078  国家自然科学基金支持

作者: 青兰*, 乌云高娃:内蒙古大学数学科学学院,内蒙古 呼和浩特

关键词: 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

摘要: 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。
Abstract: 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.

文章引用: 青兰, 乌云高娃. Riordan阵与广义λ-Array Type多项式恒等式[J]. 理论数学, 2016, 6(3): 288-298. http://dx.doi.org/10.12677/PM.2016.63043

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