何天晓.P分之一Riordan矩阵及恒等式构造[J].数学研究及应用,2021,41(2):111~126
P分之一Riordan矩阵及恒等式构造
One-$p$th Riordan Arrays in the Construction of Identities
投稿时间:2020-10-30  修订日期:2021-01-03
DOI:10.3770/j.issn:2095-2651.2021.02.001
中文关键词:  Riordan矩阵  P分之一Riordan矩阵  A序列  生成函数  恒等式
英文关键词:Riordan array  one-$p$th Riordan arrays  $A$-sequence  generating function  identities
基金项目:
作者单位
何天晓 Illinois Wesleyan University 数学系 
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中文摘要:
      本文构造了垂直和水平P分之一Riordan矩阵,这里P是大于或等于二的整数.当P等于二时,垂直和水平P分之一Riordan矩阵就是垂直和水平的半Riordan矩阵. 我们还给出了垂直和水平P分之一Riordan矩阵的A序列的生成函数.垂直和水平P分之一Riordan矩阵可以用来发现许多恒等式,并简化许多著名恒等式的证明.
英文摘要:
      For an integer $p\geq 2$ we construct vertical and horizontal one-$p$th Riordan arrays from a Riordan array. When $p=2$ one-$p$th Riordan arrays are reduced to well known half Riordan arrays. The generating functions of the $A$-sequences of vertical and horizontal one-$p$th Riordan arrays are found. The vertical and horizontal one-$p$th Riordan arrays provide an approach to construct many identities. They can also be used to verify some well known identities readily.
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