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 |
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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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